Here's mine, but I'll start with 1994. To be honest, I didn't play a lot of games that released prior to that year, so I can't really know which games should be GOTY for 1990-1991-1992-1993...
1994: Final Fantasy VI (III)
1995: Chrono Trigger
1996: Resident Evil
1997: Final Fantasy VII / Crash Bandicoot 2: CSB (tie)
1998: The Legend Of Zelda: Ocarina of Time / Fallout 2 / Banjo & Kazooie (tie, I just can't pick one between these three)
1999: Age of Empires II
2000: Baldur's Gate II: Shadows of Ann
2001: Silent Hill 2
2002: TES III: Morrowind
2003: SimCity 4
2004: Halo 2
2005: Star Wars: Battlefront 2
2006: Kingdom Hearts II / The Legend Of Zelda: Twilight Princess (tie)
2007: Bioshock / God of War II (tie)
2008: Mass Effect
2009: Uncharted 2
2010: Dragon Age: Origins (yup, liked it more than RDR)
2011: TES V: Skyrim
2012: Dishonored
2013: The Last Of Us
2014: Dragon Age: Inquisition / Super Smash Bros. 4 (tie)
This list is nothing but an opinion. Some might notice GTA is not on this list, but I never really liked GTA that much, to be honest. Same goes for Gears Of War. Great games, obviously, but I just couldn't get into it, sadly.
Making this list was a blast, I stumbled on SO many games I used to play as a child, like Star Wars: Jedi Starfighter, Medal of Honor: Frontline, Zoo Tycoon, etc...
But of all these games, which do I like the most ?
The Last Of Us and Silent Hill 2. These are my absolute favourite, by far. Even Final Fantasy VI doesn't come close, and I LOVE FF VI.