There are 17 playable characters in Isaac at the moment. (Isaac, Magdalene, Cain, Judas, ??? aka the Blue Baby, Eve, Samson, Azazel, Lazarus, Eden, The Lost, Lilith, Keeper, Apollyon, The Forgotten, Bethany and "Jacob and Esau"). The stats are shown in the image below. If you include the tainted versions of the characters then there even are 33 characters! Source [bindingofisaacrebirth.gamepedia.com]

• Isaac : Unlocked by default
  
• Magdalene : Have seven or more Heart-Containers at once
  
• Cain : Have 55 or more cents/pennys at once
  
• Judas : Defeat Satan
  
• ??? aka Blue Baby : Defeat Mom's Heart 10 times
  
• Eve : Beat two floors in a row without picking up any hearts
  
• Samson : Beat two floors in a row without taking any damage
  
• Azazel : Purchase three items from Deals with the Devil in a single run
  
• Lazarus : Have four or more soul/black hearts at once
  
• Eden : Defeat Mom's Heart
  
• The Lost (Without AB/AB+) : Isaac must die to a Mulliboom in The Basement or The Cellar.
  Magdalene must die to her own bomb in The Caves or The Catacombs.
  Judas must die to any Mom attack in The Depths or Necropolis. Being killed by any monster spawned by Mom will spoil the entire attempt at unlocking The Lost.
  Azazel must die to any Satan attack in Sheol. Being killed by The Fallen in the boss room or a Kamikaze Leech will spoil the entire attempt at unlocking The Lost. Being killed by using The Bible doesn't count as a Satan kill.
  
• The Lost (With AB/AB+) : Die in a Sacrifice Room while holding Missing Poster
  
• Lilith (Available in AB) : Complete Greed Mode with Azazel
  
• Keeper (Available in AB) : Donate 1000 Coins to the Greed Machine
  
• Apollyon (Available in AB+) : Defeat Mega Satan for the first time
  
• The Forgotten (Available in AB+):
  ● The Lamb must have been defeated previously before The Forgotten can be unlocked, and unlocking The Forgotten can be done in both Normal and Hard difficulty.
  ● First, start a new run. Defeat the boss of the first floor within the first minute. If done correctly, Mom's voice will yell, you will hear the sound of running footsteps, and the large shadow of a shovel handle will appear on the floor of the starting room. Bombing anywhere in the room will cause the shadow to disappear, and spawn the Broken Shovel Broken Shovel.
  • Holding the Broken Shovel will cause Mom's feet to continually try to stomp you. Using the Broken Shovel will stop the stomping for the current room or for the current wave of a multi-wave room, such as the Boss Rush.
  • On XL floors, both bosses must be defeated within one minute. Although this is possible, it is difficult, and it is recommended to simply restart.
  • Once you pick up the Broken Shovel, you must not trade it for another active item. If you leave it in a room and try to come back for it, it will disappear.
  • This cannot be done during a seeded run; it must be random. Mom's Voice will not trigger and you will not be able to bomb for the shovel.
  ● Next, clear Boss Rush. This will grant the second piece of the Broken Shovel Broken Shovel, completing Mom's Shovel Mom's Shovel.
  • The normal requirement for getting to Boss Rush within 20 minutes does not apply, as the hole to go to The Womb after clearing Mom will be sealed until Boss Rush has been completed.
  • After Mom's Shovel has been acquired, Mom's feet will stop attempting to stomp you, and Mom's Shovel can be used like We Need to Go Deeper! We Need to Go Deeper!
  ● Finally, in the Dark Room, find the empty room with a Dirt Patch in the center, stand on top of the patch and use Mom's Shovel to unlock The Forgotten.
  
• Bethany (Available in Repentance) : Beat Mom's Heart or It Lives in hard mode with Lazarus without losing a life.
  
• Jacob & Esau (Available in Repentance) : Defeat Mother with any character
  
• Tainted Characters (Available in Repentance) : Use the Red Key or Cracked Key in Home with each of the Characters
  ● To get a Cracked Key, simply drop a trinket in a boss or item room. It will transform into a Cracked Key when ascending