I sometimes play videogames with my arms crossed.
When I went over to a freind's house to play Super Smash Brothers: Brawl he didn't have an extra classic controller so I used the Wiimote and nunchuck, and I would lean back with my arms crossed and hanging a bit at the sides with one in each hand. Probably the only console that you can play like that, actually.
One other 'arms crossed' game I can think of was Infantry Online, where there's little mouse movement involved and the alphabetical keys are mostly for chatting. I would have my left hand on the arrow keys for movement and my right hand crossed (I forget if over or under) on the left shift/control/tab keys to shoot my weapons.
When I'm playing a more casual game or turn based game I will sometimes sit at a diagonal to my desk and lean back in my chair with my feet up on my desk, and have my left arm tucked under my knees to reach the keyboard. I also have a tendency to have one of my legs crossed under the other recently in a more normal sitting position, which I haven't noticed myself doing much before a few months ago. I have to get myself to stop doing that because it puts a lot of pressure on my foot.
In FPS games I have a tendency to spam WSAD (movement) even when things are relatively calm, making my character dance all over the place. This is primarily because I hate being sniped, and I'm always afraid that some jerk is sitting on a hill 500 meters away trying to kill me.
... I almost always mute the game. No sounds, no music.
In almost every FPS game I play I have music disabled, especially if there are voice comms or things that give enemy positions away such as footsteps. Left 4 Dead was an exception, because for the most part the music gave away what was going on before the thing even happened.
(Flight sims, docking, landing planes, etc.)
I have a tendency to manually pilot things even when auto pilot is available. I also prefer first person driving and flying in games like ARMA even if third person view is available, yet in racing games I like third person view because I don't have a TrackIR.
When I played cRPG mod for Mount & Blade: Warband I would hold my breath without realizing it during fights, and when I won/lost I would gasp or sigh when I suddenly realize that I have to breathe, hehe. I don't know if I do that for other games, but if I do it's not nearly as noticeable since in Warband a fight can last a minute or more depending on what's going on (or it could be over in one swing).
When I haven't played an action game in a long while I will be really jittery to the point where I accidentally move the mouse halfway across the pad suddenly, which screws up my aim (or gets me killed in Warband). I have to get comfortable with the game again before I can relax and play normally. Even then I'm more tense than I should be and it often causes me to make jerky movements with the mouse.
Oh, and one more thing. Rarely will I ever use the default controls for games, I always have to change them. Some people are fine with default controls, but I can't remember the last game I used spacebar for jumping, for example.