Just like quite a few other people I have played way to much of this game (almost 100h). And at some point, you want to give yourself an extra challenge. In my case that would be the "No-Evidence"-challenge, which means you are not allowed to use any gear which is used to collect primary evidence. While doing this challenge, you quickly notice that every ghost type has some very unique characteristics, some of which are even enough to identify them without any evidence. I decided to share some of the gathered knowledge here, some of which originates from the wiki as well. So, without further ado let's get started.

UPDATE:
Adding the new ghosts and will rework some of the old ones over the upcoming days.
A small disclaimer, the time i spend with the new ghosts is still rather limited, so therefore should be taken with a grain of salt.

Danger level: Wild card.
Primary Evidence: EMF 5, Spirit Box, Ghost Writing
Strength: none
Weakness: Doesn't attack for a longer time when being smudged 120 seconds .
Secondary Evidence: See Weakness.

Honestly one of the most difficult ones to identify by behaviour alone since they don't have a special behaviour apart from one: Smudge Sticks. Spirits don't attack for a longer period after you smudge their room.
Apart from that they are in my experience pretty much a wild card. They can be extremely shy to the point of not doing anything or be aggressive chain hunters. And therefor extremely hard to identify without evidence and are usually identified by the process of elimination.

Danger level: Dangerous.
Primary Evidence: EMF 5, Spirit Box, D.O.T.S..
Strength: Can travel through doors and walls, but most importantly, can see through any door (that includes locker doors)
Weakness: Salt. A wraith stepping into salt increases ghost activity and according to the wiki stops him from attacking. (never observed the latter part though)
Secondary Evidence:
Very high Activity after stepping into salt and being smudged multiple times. Rarely steps into salt and should never leaves footprints (due to flying). Rarely produces a footstep sound. Hunts you through closed doors. Technically can go through walls, but I personally never actively observed that.

These bois are dangerous, be it with their ability to see through doors alone. So hiding behind a door like in a locker or a small storage room is not going to help you one bit. Get a wall between you and the wraith, should he hunt you. According to the wiki they stop attacking (I assume hunting) when they step into salt, but I have yet to observe that. Might be because they also fly over the salt most of the time.
It also is important to note, due to their ability to fly through walls, it might be that adjacent rooms might also get colder, especially if it is in a large map with many small rooms (e.g. the asylum), so double check your rooms which one might be the ghosts room.
Apart from that, they can get extremely active if you use all the smudge sticks and salt do your disposal, easily surpassing any Oni you might find in the field.
A small disclaimer here, I have seen wraiths leave footprints, but this is rare and most likely a bug.

Danger level: Average.
Primary Evidence: Spirit Box, Fingerprints, D.O.T.S
Strength: Seeing the Phantom drains you sanity faster than usual.
Weakness: Does not attack if players stick together, or at least that is what the book says, had a few that did it anyway. Disappears if a picture of it is taken (does not stop a hunt).
Secondary Evidence:
Disappears when photographed.

Phantoms are pretty straight forward, if you take a picture and the ghost disappears it is very likely a Phantom.
Another identifier is that Phantoms blink with a lower frequency during a hunt (1-2 seconds instead of 0.3-1 second)
Apart from that they have few distinguishing features. Except for their increased sanity drain when observed.

Danger level: Average
Primary Evidence: Spirit Box, Fingerprints, Ghost Writing
Strength: Likes to throw a lot of stuff around and according to wiki thrown stuff drains sanity even if you can't see it.
Weakness: None. Technically can't make use of it's strength in an empty room, but who the hell cares to clean out the room in the first place.
Secondary Evidence: Interacts with a lot of physical objects including doors and light switches.

Poltergeists tend to play with everything they can get their ethereal hands on, that includes light switches, phones, doors, etc.
So, in that sense, while it prefers to throw stuff it also touches everything else. In fact, according to the wiki it is the only ghost that can throw multiple things at once.

It can be hard to distinguish it from a Jinn, since both can be quite playful with phones and light switches.

Danger level: Very dangerous.
Primary Evidence: Fingerprints, Ghost Orbs, D.O.T.S
Strength: Can spawn basically anywhere when hunting (more in text below) and at any time (can ignore sanity).
Weakness: Always has 1 target and will ignore other players if hunting. Crucifix has a 9m radius instead of a 3m one.
Secondary Evidence: Never changes its target unless target dies or exits the building. Can start a hunt despite extremely high sanity.

Banshees are vicious. If they make use of their power, they will make their way towards a selected player and when direct line of sight is established, she will wait a short amount of time and then start a hunt from that position. If she uses her power, she also ignores sanity. This means she can in theory hunt from everywhere at any time. The only saving grace for the players is that she ignores every other player apart from her target, which also serves as a sure identifier for her. Her ability can also cause a red herring, since she doesn't have to spawn in her room.
It is advised to always make sure that you are either close to a deployed crucifix or a good hiding spot.

Danger level: Dangerous
Primary Evidence: EMF 5, Spirit Orbs, Spirit Box.
Strength: Faster the further it is away from its target.
Weakness: Technically none to speak of. Can't use its ability if the breaker is turned off (nearly nobody does that, and this only sets him back to be like any average ghost).
Secondary Evidence: Closes the distance to a visible player quickly but if close (about 3m) slows down to the speed of a player. Turns the breaker on more often than other ghosts. Prefers to interact with electronics. Rarely turns off lights or breaker.

Even though Jinn’s are dangerous, they tend to be my favorite type of ghost to hunt. Well technically they are dangerous should they ever hunt, but due their habit of rarely turning off lights and the power, sanity tends to stay quite high, meaning very few hunts.
In addition, this habit also makes them easy to identify without any hard evidence or even a hunt. But the easiest way to identify a Jinn is to observe its behaviour during a hunt: If it closes the gap quickly and then slows down when it is close, it is a Jinn. This can also be heard, in that the footsteps are faster.
Another very unique identifier is that it is the only ghost type that somewhat reliably turns on the power again and rarely turns it off. While other ghosts tend to do that extremely rarely as well, with a Jinn it usually is a sure thing that he will turn on the power eventually.

Danger level: Above average.
Primary Evidence: Freezing Temps, Orbs, Spirit Box.
Strength: It hunts earlier if the ghosts room is in the dark (at 60% average sanity) . Turns off power and light frequently.
Weakness: Next to none, due to Habits. Hunts less if the ghosts room is lit. (at 40% average sanity)
Secondary Evidence: Turns off lights and power extremely often. Tends to hunt very often due to the resulting sanity loss.

Mares... I hate them. Not only turn they off the lights and power all the time, they also hunt early and often. They like the dark and it shows.
It also is important to note, that this habit has a strong impact on players sanity which will make a Mare hunt relatively early. This only gets emphasised by the fact that a Mare hunts more often if it is dark. Candles can help to counteract the darkness somewhat (they need to be placed down, when carried they don’t have sanity saving properties).
At least this habit alone makes them quite easy to identify without any hard evidence. But it is still important to be able to distinguish if the ghost turned off the breaker or if the players just overloaded it by turning on too many lights. Usually you can distinguish this by checking if all light switches turn off at the same time the breaker is tripped, or if the lights turn on again as soon as the breaker is fixed. If the switches turn off, then it was the players’ fault.

Danger level: Extremely Dangerous. (you may hide, but not run)
Primary Evidence: EMF 5, Ghost Writing, Fingerprints
Strength: Extremely fast if a target is visible for it.
Weakness: Very slow if no target is visible.
Secondary Evidence: See Strength

Due to their power, Revenants are extremely dangerous. If they can see you, they will get you. Your only chance will be to break line of sight and hide ASAP. But given that the devs plan to implement that ghosts will try to search players at their last seen location, will make those ghosts far more dangerous than most others in the future. A smudge stick may help in an emergency.
Sadly, this behaviour is the only unique secondary evidence it has and collecting this evidence is often paid for with a life. Therefor I recommend distinguishing this ghost by the process of elimination.

Danger level: Average
Primary Evidence: EMF 5, Orbs, Ghost Writing.
Strength: Low activity if multiple players are near.
Weakness: Will rarely start a hunt if players are in the same room.
Secondary Evidence: Low activity 3+ players are in the room, high activity if only 1 player is in the room.

Shades are quite elusive ghosts. Their habit of having very low activity when all 4 players are present makes them hard to find and even harder to identify without any hard evidence. But it should also be noted that they can have a rather high activity if only one player is present, sometimes even rivalling an Oni. In that sense they are much like a reverse Oni, in that they get more active the fewer people are near.
It also is important to note, that with player proximity is usually defined by being in the same room. This means that a player outside the door, even if he is less than a meter, away counts as alone and therefor making it more likely to trigger a hunt should the average sanity already be low.
Also, it seems to only lower the chance of a hunt if players are together, it won't prevent it from hunting.
All in all, this behaviour makes it nearly impossible to distinguish from other ghosts, since it is extremely hard to notice.

Important to note, number of players in a game has no effect on the ghost. This means if you play solo a shade might be as active as an Oni.

Danger level: Above average
Primary Evidence: Freezing Temps, Spirit Box, Ghost Writing.
Strength: Hunt earlier (65% average sanity) and more often.
Weakness: Doesn't drain sanity if it answers to a question on the Ouija Board.
Secondary Evidence: See Strength.

Demons are extremely aggressive, and therefor hunt earlier than most and more often than most. Using an Ouija board doesn't drain sanity if it answers, but it will still drain a high amount of sanity if it should refuse to answer (light flickering even if the breaker is off and the board turns off).
Even though you would think those 2 facts make it easier to distinguish, it is not. I have seen many ghosts that were even more aggressive than a demon and the normal sanity loss of a few percent is barely noticeable.
So, it is recommended to use the process of elimination if no primary evidence is found.

Danger level: Average
Primary Evidence: Freezing Temps, Orbs, Ghost Writing.
Strength: Drains Sanity quicker than other ghosts
Weakness: None to speak of.
Secondary Evidence: Tough luck, if at all faster sanity loss.

If it wasn't for their freezing temperatures, Yurei’s would be indistinguishable from a normal Spirit, especially since any sanity loss is extremely hard to notice.
Due to them draining sanity faster than other ghosts they seem to hunt very early. So one way to distinguish a Yurei from other ghosts would be to be conservative with your sanity and check sanity after a hunt. If you sanity is unnaturally low, it might be a Yurei.
But apart from that, there is no other way to identify a Yurei by behaviour alone.

Danger level: Average
Primary Evidence: EMF 5, Spirit Box, Ghost Writing.
Strength: Very active the more players are close
Weakness: None to speak of.
Secondary Evidence: Extremely active if all players are close.

Onis will rip apart any room they are in if all 4 players are in there, even without using smudge sticks. This fact makes them relatively easy to identify. But keep in mind it is barely active at all if there is only one player close, even less active than a Shade might be. That said, they are pretty much a reverse Shade.
A small disclaimer: Higher ghost activity also means that they hunt more often than other ghosts as well.

Important to note, the total number of players does not affect this ghost either. If playing solo, an Oni will barely do anything.

Danger level: Average
Primary Evidence: EMF 5, Fingerprints, D.O.T.S.
Strength: Will usually only show itself on camera when nobody is around.
Weakness: Does not move far from its room
Secondary Evidence: See both strength and weakness.

If you go by the book entry, Goryos are ghost sloths. They don't move much, they are too lazy to show themselves, not even triggering the D.O.T.S. Projector (unless seen through a camera).
One would think that this should make it rather hard to identify a Goryo by its behaviour alone. But them not moving far from their ghost room is a very strong giveaway, especially during hunts and on larger maps. Cause while other ghosts will sometimes go on a fieldtrip and rummage through the whole building, a Goryo keeps its activities rather localised. This not only is a strong giveaway of what it might be, but also where its room is.
Technically it not showing itself unless it is on camera could be a giveaway as well, but you might also just deal with very shy ghost (e.g. A shade). So this should only be taken into consideration if the ghost already has a very high activity level.
If you are using evidence gear and you can see a D.O.T.S. Projection without a camera, you can be certain it is not a Goryo.

Another thing that I noticed was, that in the few runs I had with Goryos they were insanely active and basically ripped apart the room. Not sure if that is actually a special behaviour of them or if it was coincidence, to take it with a grain of salt.

Disclaimer:
A Goryo still can manifest and be visible to the naked eye, especially during hunts. Manifestations are just relatively rare from what i can tell.

* To be added, haven't had enough experience with them yet.

Danger level: Average
Primary Evidence: EMF 5, Fingerprints, Ghost Writing
Strength: None to speak of (still makes sounds during hunts).
Weakness: More paranormal sounds through parabolic mic
Secondary Evidence: See weakness.

Disclaimer: I haven't seen many Mylings yet, so take anything I say with a grain of salt.

I absolutely love this one. Overall they are usually very active ghosts and roam a lot, which can make it difficult to pinpoint their room, but also makes for a really fun experience.
This only gets better when you pick up a Parabolic Microphone, cause then they actually start to be quite chatty, in that you can hear all the paranormal sounds they are making. This also serves as a very clear indicator if you are dealing with a Myling or not, since the sounds are a lot more frequent than with other ghosts.
Normally i would say that their silent hunts would be a dead giveaway as well, but currently they are just as noisy as any other ghosts, but I assume that is going to be fixed rather sooner than later.

* To be added, haven't had enough experience with them yet.

Thanks a lot for reading and I hope it helps in your ghost hunting adventures. Should I have forgotten any important details, let me know in the comments.
PS: Let me know in the comments if you would be interested in this to evolve into a full guide.