The games I'd most recommend to become a well rounded game connoisseur such as myself.

- Super Mario RPG (1996)

- The Legend of Zelda: Majora's Mask (2000)

- Silent Hill 2 (2001)

- Sonic Adventure 2: Battle (2001)

- Metal Gear Solid 3: Snake Eater (2004)

- Paper Mario: The Thousand-Year Door (2004)

- Sam and Max: Save the World (2006)

- Batman: Arkham Asylum (2009)

- The Walking Dead: Season One (2012)

- Assassin's Creed IV Black Flag (2013)

- Dark Souls 2 (2014)

Recommended to be played on original hardware where most applicable, emulation is poverty.
I've only added games I've actually completed, maybe there's more culture out there, who's to say.