As I am of the opinion that different games, different genres and different consoles are variables that provide an experience incomparable to each other, I decided to create a list of my favorite games depending on what factors are present (i.e. gaming console or whatnot that's used and whether it's multi-player or not).
PC:
My favorite PC single-player RPG game is
Planescape - Torment.
My favorite PC multi-player RPG game is
Diablo II: Lord of Destruction.
My favorite PC single-player FPS game is
Half-Life 2.
My favorite PC multi-player FPS game is
Unreal Tournament 2004 [Team Fortress 2 and Counter-Strike 1.6 are close, though I almost never play them solo]
My favorite PC single-player RTS game is
N/A.
My favorite PC multi-player RTS game is
Warcraft 3: The Frozen Throne.
My favorite PC single-player TBS game is
Heroes 3: Complete.
My favorite PC multi-player TBS game is
Heroes 3: Complete.
Edit: forgot a genre I play.
My favorite PC single-player third-person shooter game is
Hitman: Blood Money [or Hitman: Codename 47 or Contracts].
My favorite PC multi-player third-person shooter game is
Rune [although Jedi Knights: Jedi Academy is a close second].
Consoles:
My favorite SNES single-player game is
Super Mario Bros. All-Stars #3.
My favorite SNES multi-player game is
Joe & Mac - Cavemen Ninjas [co-op].
My favorite PlayStation single-player game is
Final Fantasy VII [Rayman is a close second].
My favorite PlayStation multi-player game is
Tekken 3.
My favorite N64 single-player game is
Zelda: Ocarina of Time.
My favorite N64 multi-player game is
S.C.A.R.S.
My favorite PS2 single-player game is
Final Fantasy X.
My favorite PS2 multi-player game is
Tekken 5 [Fight Night 3 as second].
Lastly, my favorite board-game is
chess.