If I pretend I just like adventure games these would be my favourites:

Grim Fandango
Monkey Island (any one of them)
Day of the Tentacle
Sam & Max (try the new ones as well)

A lot of LucasArts games. Well, 100% is a lot.

And while I have your attention (hopefully), try Europa Universalis 3! Great game.

I don't think I can pick a genre to be my favorite. I love RTS games, (Long live Kane!) but I also love to play FPS games. Adventure games and RPGs are great too.

I was addicted to X3: Reunion and the mods it spawned for six months. that was fun not much for shooters, though. I get bored after a while

Picking a genre is tough, because I like variety.

Some favorites.

GTA3
Half-Life 2
Oddworld: Stranger
Jet Set Radio Future
Halo 3 (for the multiplayer)
Starcraft.
FF7
Rollercoaster Tycoon

Sim/Tycoon games
World of Warcrack
Privateer II
Final Fantasy(s)

I'm a huge fan of fighters, RPGs, and DDR.

Favorite games:

Chrono Trigger
FF VI
DDR Extreme 2
Smash Brothers
Smash Bros. Brawl
Marvel vs. Capcom
Pokemon Yellow (lol)

WoW
C&C series (Kane's Wrath is way cool, but the original Red Alert is probably my favorite of them all)
Starcraft
Dungeon Keeper (Make a third one EA!)
Peggle (It's so damn addictive)
Freelancer
Max Payne 2; (and the first one too)
Transport Tycoon is fantastic
UFO: Alien Unknown (or X-Com)
Heroes of Might & Magic 3

kulpims: I tried X3 as a replacement for Freelancer, but I thought it was pure shit. The instant I flew through a building, that game went on the pile of rejects. (Even payed for it too, damn you starforce, you made may pay for a crappy game!)

Oh and Diablo 2! Damn, I lost a lot of hours to that game.

When it comes to video game genres, I don't discriminate, as long as there is more enjoyment than frustration to be had out of it. Currently playing : Ninja Gaiden DS (best action game for the DS by FAR, kudos to Team Ninja for pulling it off and making it look easy), Advance Wars: Days of Ruin (the pre-eminent turn-based strategy series, non-PC-wise and also for the DS), and Smash Bros. Brawl. My PC is in desperate need of an upgrade or flat-out replacement so I've been missing out on nearly everything post-TF2 though I still occasionally dabble in WoW. As far as past games go, many have already been mentioned above; you guys are gamers after my own heart!

EVE Online is about the only game I consistently play right now.

Some older favorites:

Neverwinter Nights and Expansion packs (One of the best game experiences ever especially Hordes of Underdark, NWN 2 was disappointing)

Sacred (This was like Diablo set in a larger open world, I actually finished this game 3 times)

Counter-Strike 1.3 (after that and Source it wasn't the same at all - The AK47 was so awesome in this version)

Quake 1, 2, 3. - Bots, Multiplayer and gibs. Nuff said.

Unreal Tournament (The original is still the best, UT3 was a huge consoley disappointment)

Freelancer 1 & 2 (Anyone remember pulling GTVA space patrols in a nebula? It was my own personal BSG)

Transport Tycoon Deluxe (Laying roads, train tracks, air and sea transport routes, was never so much fun, Locomotion was a huge disappointment)

Jagged Alliance 1 & 2 (Squad control mercs! Ivan Dolvich was hilarious)

Ivan Dolvich: You do not speak Russian? Ah, I miss days when Russia was at war with everybody.
Ivan Dolvich: [Speaking Russian; after killing an enemy in a rather brutal way] And that's why my nephew is an alcoholic.
Ivan Dolvich: [Speaking Russian; upon finding a weapon he likes] If I keep quiet, I will be able to keep it for myself!

Soldner (Like a JA clone set in a pulpish WW2 setting)

UFO: Alien Unknown (Oh my god this game was so scary, especially when you started getting Psiattacks from the aliens, still unrivaled today, even though countless companies tried direct copies, I didn't really like X-Com because of the underwater setting)

Heroes of Might & Magic 3 (I loved the 2D graphics, the newer 3D one isn't as magical nor did it have near the amount of units/artifacts/heroes as HMM3)

Rise of Nations (This was really one of the best and most enjoyable RTS games I ever played)

Total Annihilation (Visceral, primal RTS combat with robots, Supreme Commander lost that magic touch)

Morrowind (Oblivion was good but not as good as Morrowind which had more of an open ended feel, and not as consoley based as Oblivion)

I would say my favorite genre is FPS, though so far all am looking forward to is Fallout 3 and Jagged Alliance 3/3D/4 (if it ever makes it), I was looking forward to a shooter that was said to cover all the weapons from the 20th to 21st centuries following a familial history but I forgot the name, it had a really cool trailer too.

^ UFO: Enemy Unknown is X-Com: UFO Defense, they just renamed it for the USA market, unless you mean part 2 "Terror From The Deep".

I love adventure games, RPGs, strategy, and lately more FPS games

My favorite games of all time are:

All-time favorites:
Fallout 1 & 2
Final Fantasy III (Part VI in Japan)
Ultima Online (at least from '98 until '03, it sucked after that)

Other favorites:
Wing Commander I-IV, Prophecy, Privateer I & II
Day of the Tentacle
Full Throttle
The Dig
Sam and Max Hit The Road
Star Trek 25th Anniversary & Judgment Rights
Gabriel Knight: Sins of the Fathers
Police Quest I & III
Space Quest I, II, III, IV, & V
Kings Quest IV & V
EcoQuest: The Search For Cetus
X-Wing, Tie Fighter, X-Wing: Alliance
Star Wars: Rebellion
Star Wars: Dark Forces I & II
Star Wars: Knights of the Old Republic
Civilization IV
Ultima VII: The Black Gate
Deus Ex 1 & 2
BioShock
Half Life 2 and its Episodes
Zork
Planetfall
Syndicate
and I'm still probably forgetting a handful...

I still play Master of Magic for the PC, love that game. Also, still playing Transport Tycoon regularly.
Finally, on the console I've been a proud owner and player of Populous since its 1990 release. But really, anything from the NES, Megadrive and SNES tickles my fancy as that period of gaming history was when I actively played games.

Some of my favorites, old and new:

Console:
Zelda series
Final Fantasy series (VI remains my favorite to this day)
Dragon Warrior
Metal Gear Solid
God of War/2
Punch Out/Super Punch Out)
Metroid (the old classic 2d side-styles, not the 1st person view)
Gran Turismo
Shadow of the Colossus

PC:
Outlaws (Old West FPS from Lucasarts)
Diablo 2
No One Lives Forever
Oblivion
Sim City
Half-Life series (Portal included!)
Wing Commander 3 (yay, Mark Hamill found work!)
Alone in the Dark
Out of This world
Age of Empires series

I mostly play simulators and first person shooters. Here are some of my favorites that are still on my software shelf:

Flight Simulators:
MS Flight Sim
Falcon4: Allied Force (no time to play anymore)
IL2/Pacific Fighters

Racing:
Richard Burns Rally

Realistic FPS:
Operation Flash Point
Armed Assault
Hidden & Dangerous 2
Rainbow 6 Series (Everything after Raven Shield has sucked though)
SWAT 3
SWAT 4

Other FPS:
Half-Life
Portal
Hitman
Call of Duty Series
S.T.A.L.K.E.R Shadow of Chernobyl
Dues Ex
Kingpin
No One Lives Forever
The Chronicles of Riddick

Multiplayer:
Battlefield 2
Team Fortress 2

Other:
GTA: 3/Vice City/San Andreas
Civilization 4

Anything my Sega Genesis has had in it in the last week would qualify as a favorite.

E.T. for the Atari 2600

I like to play "bury the bone", "hide the hot dog", and "cram the kielbasa". Also, I like to play "flog the dolphin" and "serenade the skin flute" when I'm in solitude.

My favorite genre is usually straight one on one or two on one (not the "devil's threesome" though). I can get down with a little bit of slap and tickle but too much is distracting. Deep and slow or fast and hard, either way, I'm down.

Oh...video games? Oh, I told you already, I'm still playing "River City Ransom". Seriously...

My favorite genre are probably murder simulators I mean FPSs. Nothing beats good ole multiplayer mayhem, be it team play or death match. My current favorite is TF2, not only is it great fun, but it doesn't bring my computer to its knees and make it beg for mercy. Q3 gets an honorable mention for all the countless hours of LAN games I played on it.

Other Games I've enjoyed greatly:
Final Fantasy 3 (US)
Secret of Mana
Chrono Trigger
Grim Fandango
Star Craft
Galactic Civilizations II (Known to cause highly localized time warps)
Half Life series

I've recently managed to kick a WoW addiction, I'm treating it with a plethora of other games to manage the cravings.

Also
>> ^blankfist:
E.T. for the Atari 2600

^Masochist

I used to love rts/strategy type games (C&C, Dune II, Civilisation, Railway Tycoon, Syndicate etc. etc.)

However now that I have a job, and a family etc. time is seriously limited for game playing, so I've turned to games that give instant fun and can be picked up and put down quickly... so FPS is where it's at for me. Bioshock and the Half Life 2 games are my current lot.

The Crysis demo was pretty awesome too, but seeing as I've owned the orange box for months now and haven't even started HL2 ep2, I can't justify buying that... or Gears of war for the PC for that matter.

So I still do love an RTS and other such games (in my youth I LOVED adventure games, not so much now)... but time somewhat dictates what I can play.