Obs. This does not apply if you already knew that the story in the previus game wouldn't affect the sequel (Bad Company 2 or any Final fantasy game for instance.).

I bought Jak 2 when I was 10 without ever having played the first. I think it actually took my until after I had completed Jak X (well, as much as I could complete before it corrupted my memory card) that I bought Precursor Legacy.

half life 2
halo 2

Skate 2, Far cry 2 and load others

NWN 2. And soon, AC2.

Saints Row Two and Fallout Two, but I have only recently gotten into gaming and SR2 was inspired by Yahtzee more than anything else.

I actually go Fallout Three before two, but I have yet to play one so I think it counts.

Fallout 3, if it counts.
Tomb Raider 3 as well.

Well yes actually.

I played C&C 3 and it's expansion without ever knowing anything about the first 2 games.

Halo, 3, Gears 2, Skate 2, Sonic Battle Adventures 2... And those are the ones in my room.

Half Life 2

Saints Row 2

Far Cry 2
(I did play the first one after I played the second one though)

Halo 2

And many more...

Baldur's Gate 2, Hitman 2, GTA: Vice City, Fallout 3, Team Fortress 2, Counter-Strike: Source, The Elder Scrolls 3: Morrowind, Rainbow Six 3: Raven Shield... And surely a bunch of others I'm forgetting.

Hitman 2 and 4. Because the other 2 games weren't rated highly.

Half Life 2, though I played the original when it was later on sale for 98 cents (10 year anniversary).
Fallout 3, though some fans would argue it doesn't really count.
Sly 2.

Resident Evil 2; though later went back and got the first as well.

Formula 1 '97, Half-Life 2, Fallout 3, Call of Duty 3 (though I'd played later ones before I bought it :P).

These are the only ones I remember, probably a couple more I've forgotten.

Far Cry 2, Assassins Creed 2, Half Life 2, Metal Gear Solid 2, and some other PS2 games, cant remember

Tenchu Z, FF8 without 1-7, CoD2, Castlevania: DoS, many more

Yes for me it was crash bandicoot 3,teken 3,and Maximo vs the army of zin.

The Orange Box. I started w/ Half Life 2, but I think I went through it ok w/o knowing what really happened in Half Life 1.

Fallout 3

System Shock 2

Warcraft II

Elder Scrolls 3

A Crash Bandicoot Game

Jet Set Radio Future

Half Life 2 (eventually Played Half Life though)

Parasite Eve 2

AvP2, BIAHH (Hell's highway, if my acronym makes no sense), Civ4, Fallout 3 and TF2.

Half Life 2, Team Fortress 2, Elder Scrolls 2, Valkyrie Profile 2, Phantasy Star 2, Double Dragon 2, Dragon Quest 8 (played older ones, but not 7, the previous game), Breath of Fire: Dragon Quarter (ditto), Metal Gear Solid 3 (ditto ditto), etc..

Devil May Cry 3, Sly Racoon 2, SSX3, Spider-Man 2, Timesplitters 2, Grandia II, Pac-Man World 2 and Ratchet & Clank 3 (in which case I owned the first game, but had never ever seen the second).

Elder scrolls IV
GTA IV
Crisis Core Final Fantasy IV (prequel so it may not count)
Fallout 3
Im sure theres more I just cant think of them at the moment

I got half-life 2 before I got the original half-life.

I got GTA 3 having never played ay other gtas before it.

I got resident evil 5 before I'd ever played any other resident evils.

That's about it.

half-life 2
GTA IV
Fallout 3
Saints row 2
Elder scrolls IV
Warcraft 3
Resident evil 4
Team fortress 2
Far-Cry 2
Gears of war 2
Red faction: Guerilla

And this is probably less than half

I think the only time I've ever done this is with Resident Evil 4, which doesn't really rely on the earlier games at all; besides I knew enough about them to know who Wesker and Ada were for example.

Other than that, I pretty much never play a game until I've played the earlier ones if they build on one another. For example, I got Banjo-Kazooie: Nuts and Bolts as a gift, and went out and played the first two games first to make sure I got the jokes and references. Turns out there wasn't as many references as i though, but the games were fun so thats OK.

The Elder Scrolls III: Morrowind
Fallout 3
Legacy of Kain: Blood Omen 2
Doom 3
Quake 4 (without playing Quake 2, I played the first though.)
Thief 3: Deadly Shadows

I jumped into the Silent Hill series with Silent Hill 3. Then went to play the rest. Not exactly the best decision for a newbie to the series, but it worked to hook me permanently and the series is now one of my favorites.

I have never played Metal Gear Solid (the original). I started with MGS2. I own the 3-game collection for PS2 now and will be playing that original MGS soon.

sure.

I played mario 1-2 and, and then 64 so i guess i missed 3 through 63...

BG2, RES4, Metroid prime3, and prolyl several others i can't remember.

Left COD4 and stuff like it out, cause the games are non-contiousus as far as i know, they're a new installemnt, not sequels.

Furburt:

Aliens Vs Predator 2

This one doesn't really matter. AVP2 doesn't really have any story connection to AVP.

Kotor 2

Dynasty Warriors 5

Onyx Oblivion:
FF8 without 1-7, CoD2

Final Fantasy and Call of Duty games don't really matter as each one is pretty much stand alone.

The Modern Warfare Call of Duy games are the only ones that actually connect to each other on a storyline level, and even then you don't really need to have played COD4 to enjoy MW2, as MW2 only makes a few references to MW's plot(the nuke going off being a big plot point).

In fact, even in the WW2 games, the only real connecting factor if there are British, there's always a Captain Price and he's pretty much a walking badass who can't die.