Yes, a lot. I easily get bored by a game, and so I change to a new one.
Currently I am playing Fallouy 3, Valkyria Chronicles, Prince of Persia and Siren: Blood Curse.

Yes I do but they have to be pretty different. I couldn't play two FPS at the same for instance! Right now I'm playing R2, TRU and sometimes other games I need to finish, mainly motorstorm 2 or buzz.

Generally one at a time, but when I got Chains of Olympus on PSP, I was playing that alongside Prince of Persia on PS3.

Often, I get fed up with a game and switch to another, only to switch back a while later. A prime example is when I was playing LBP, didn't really like it to start with, started playing Far Cry 2, hated it, went back to LBP, love it.

Before installing Win2000 on the desktop I was playing Morrowind and Temple of Elemental Evil on Win ME, after I started Thief III and despite its flaws it sucked all my gaming time, so I didn't reinstall either MW or ToEE, but after a while I started Planescape: Torment and started playing Thief III more and more rarely, finally I patched P:T in a way I suspected was breaking some dialogs, so I reinstalled it on the notebook and now I'm only playing it. Only on the Intellivision, with no savegames, and so no continuity, I managed to regularly play more than one game in a given period, when there is a complex plot, and so savegames, a game soon prevails on every other until I finish it.

I prefer playing just one game.... but I rarely do (I do consider consoles, PC and handhelds as 3 separate kinds though)

I play multiple games during a period of time.

Right now it's:

PS3
CoD: WaW
GH:WT
PoP

Edit: forgot to add Fifa 09.

DS:
FF4

and I'm planning to pick up the orange box for PC and Chrono Trigger for the DS soon.

I play 1 game per console/handheld mainly cause I can't be bothered to change what's in the console. So right now I am playing only Mario Kart (Wii), Fallout 3 (360) and Advance Wars Days of Ruin (DS).

I play approximately 3.69803 games at a time. Give or take a hundredth of a thousandth of a point.

I try and diversify what I'm playing. So I'll play one story driven game a la FPS or RPG and then one multiplayer heavy game at the same time. That way I can get a mixed set of feelings and not just play a multiplayer game forever :)

I usually try not to play more than one game on console and one on handheld at the same time, because when I start a new game while I'm playing another one it usually results in playing only one of the two after a little while.

The problem is that I am so hardly trying to follow this rule that I sometimes play nothing at all. This was the case in last december when I actually would've had a lot of time to play games, but I was in the middle of FF V and did not want to play it although I felt I have to finish it first before I start something different. So I played nothing until I started Wario Land after Christmas.