It depends on the game type.

Games with long stories get played one at a time, so Valkyria Chronicles, Tales of Symphonia, Legend of Zelda, those types of games get played 1 at a time. However, long handheld games get played whenever I'm out and not at home, so they follow a 1 handheld game at a time.

Games with short play times and little/no story get played whenever. So games like SSFII:HDRemix, Mario Kart Wii, Burnout Paradise, Mario Party 8, those types of games get played whenever I get the urge.

Now that I think about it:

Elder Scrolls III: Morrowind (started, died, forgot to save, havent played it since)
Shadows of the Empire (N64) (halfway through, couldnt beat boba fett)
Resident Evil 4 (PC) (got to Salazar, lost the will to play)
Star Wars Rogue Squadron III: Rebel Strike (got to some y-wing bomber mission, couldnt figure out what to do, quit)
Breath of Fire (GBA) (got to some gold city or maybe it was the ghost town, got stuck)
GTA: San Andreas (PC) (got to the flying school, couldnt get past destroy targets, cheated to get past it, lost will to play)
Road Rash 64 (N64) (beaten before, restarted, cant get past races 5,7, and 8 on level 5)
Jet Force Gemini (N64) (great game, got to some grave yard level, couldnt figure out what to do, quit)
Donkey Kong 64 (N64) (cant beat last boss)
Diddy Kong Racing (N64) (cant beat last boss)
GoldenEye 007 (N64) (cant get past the train level)
Super Mario 64 (N64) (hated the controls, gave up after 20 stars)
Star Wars Rogue Squadron: Rogue Leader (N64) (cant get past the Kessel level)
F-Zero X (N64) (too put in plainly, just too hard)
Ridge Racer 64 (N64) (doesnt make sense, i have beaten like 20 races and havent unlocked any new ones wtf)
StarCraft 64 (N64) (too much slowdown, almost unplayable)

I think that's it.

one at a time it to hard to go back and forth with different controls schemes
plus i want to fully enjoy the game b4 i go on to the next

i agree with nordlead game like sports and no stories i can mix them in while playing a big story driven game

I always get bored with one game, then I go one to another.

Sometimes I have a bunch of games that I haven't beaten, and that's when I go back and beat them.

Always played multiple games at any given time, but at the moment everything revolves around Left 4 Dead +1

one game at a time along with some multiplayer games i.e counterstrike, TF2 etc.

I thought you meant play them simultaneously.

Which I still do: I have dual screen monitors and frequently play Chess or Word Racer whenever I die in L4D, and I have the Bejeweled addon in WoW, which interlaces a game of bejeweled over the screen.

that 20-25 second wait to respawn when playing as the infected is Left 4 Dead is a blessing, gives me time to get another beer from the fridge

I play Resistance 2, MGS4, GT5 Prologue and Uncharted at the moment.

It doesn't happens too often, that I finish a game from the beginning to the end without playing something in between. (Assassins Creed, Bioshock, Call of Duty 4)

Usually I like to focus on one game, but I have some games I still haven't finished and want to be done with, so I'm playing multiple games ATM. I hate doing that since it makes me rush through things. Consoles at home, handhelds whenever I go out.

PS2:

Xenosaga I
Odin Sphere
Eternal Poison
Digital Devil Saga (love this game)
Kingdom Hearts: Chains

PS3:

Resident Evil 5 demo

DS:

Final Fantasy IV
Chrono Trigger

360:

Lost Odyssey
Ninja Gaiden II