I may sound a bit strange here since I'm 13 but Pokemon Red is my favourite old game. I would say Minecraft is my favourite modern game.

Most of these are series, so assume I am talking about a lot of them when I mention a single game.
Blizzard series (Not WoW), Minecraft, Terraria now, Assassin's Creed, Zelda, Metroidvania games (both series), Wizardry something for PS2, Champions of Norrath (PS2 hacks and slashes) Rock Band used to be fun, Halo was good (main 3 mostly) Might and Magic 6, 7, and 9, Submarine Titans, Doom 3, Oblivion, Master of Orion 2, PopCap Games, Space Rangers, Portal, Half-Life... and many more. My shelves of games for every system tell that story. I would need to look at my games to remember them all (i did for the PC ones). I hate when a game does not have a storyline though. Unless it is specifically designed not to. Plants vs. Zombies, Hilarious, Halo, had a good story for a while, Diablo 2, epic, Oblivion, Haven't even finished it, Fallout, cool, space rangers, surprisingly deep, portal, cake, the list goes on. Everyone should fight for better stories in games, because that is what takes a lame CoD3 and makes for a memorable CoD4, and other stuff. /~rant

Diablo I&II
Master of Magic
Heroes of Might and Magic (any)
Hide and Seek
Kick the kid holding the can
Underwater basket weaving
Halflife I&II (and Blue Shift, AND Opposing Force)
Twisted Metal (any)
Pinch the girl and run away faster than her
Avoid the doodoo
Unreal

Though I don't like referring to them as games, the Myst series is my favorite. I've played every iteration of the legendarium except for realMYST, and love every one of them. The vast array of worlds with beautiful architecture and unique landscapes that make the experience unforgettable, and the expansive storyline is both intriguing and inspiring.

Another one of my favorites is Cave Story. Smooth controls, charming graphics, tons of weapons, and best of all - FREE!

But of course, Minecraft occupies most of my free time right now.

My favorite game was Counter-Strike : Source , After two years of playing , I got WoW for so many years , But now my Total favorite game is Minecraft !

Space Invaders... Duck Yeah!

For me it has to be metal gear solid 1, then again all of the metal gear series. Other than that final fantasy 10, i just fell in love with that game and ofc it featured blitzball, whih reminds me, who will make a blitzball stadium first in minecraft?

Modern Day-ish
Call of Duty 4: Modern Warfare, Elder Scrolls IV:Oblivion (soon to be superseded with Skyrim), Mass Effect 2, Dragon Age Origins

Previous
Pokemon Yellow, Age of Mythology, Heroes of Might and Magic I & II, Sonic Adventure

... I seriously have too many to count, but those are some that stick out, (and Minecraft of course! )

Other than minecraft,Fire Emblem(The Sacred Stones)All are the best Strategy games ive ever played

COD 4, MW2, Just cause 2, Fallout New Vegas, Crysis 2, assassins creed brotherhood
Upcoming: Battlefield 3, MW3, Assassins creed revelations

CoD 4.
Mw2.
Blops.
Mc.
WoW.
Tf2.

Mhhh...


Yay for abbreviations!

All time would probably be "Castlevania: Symphony of the Night" for the Playstation; a great blend of a 2D platformer and RPG (only one other game has really come close in my eyes).

For multiplayer it would probably be TF2; I've put so many hours in to that game it's ridiculous. Then, like many others, can't forget about the Ultima series (except IX). I actually liked Ultima VIII alot, even if it seemed to be a bit too different from the rest of the series. Ultima IV and VII were probably my favorites though, Ultima V would have been but some of the story and progression in that game were just a bit too obscure and difficult to find so it got frustrating at points.

the Ultima series (on my Commodore 64!), Wizard (which was a Jumpman kind of game on the commie 64, but you could create your own levels), The Sims (because I like to watch them die) and I like Kirby's Epic Yarn, although I'm told it's the suckiest of the series (I never played the others.)

My firends and I always used to mess around on Age of Mythology

in the day mine was age of empires 2 i played it every time i got home from school

Call Of Duty 4...that is all.

Metroid Prime Hunters was awesome

Ultima IV Commodore 64

Zelda series, Metroid (especially Metroid Prime), Pokemanz
They were the games I played through most of my childhood.. and sometimes still play today, lol

BACON

Other than Minecraft, I'd go oldschool and say Chrono Cross.

Old time...um, does SSBM count?
Modern....definitely BRINK.
AND OF COURSE, I play Minecraft.