I usually sit in a couch potato way having one hand forming a L on my chin.
chess face

http://www.chess.com/forum/view/general/greatest-chess-photos contains some pretty famous 'stares'. When I look at some of those faces, I couldn't imagine sitting across from them for four hours.

I have a strait face and one hand on my face; with a thumb below the cheekbone and fingers holding my glasses in place because my head becomes tilted.
My concentration face is apparantly a mix of surprise and anger. Perhaps this caused some of my opponents to think I was lost and they underestimated me?
My concentration face... well you can't see it. If I'm really in such a bad position that I must concentrate, then your eyes most likely will have been gouged out, and you'll still be unable to see my concentration face.

There's a cookie in that picture!!!!!!!!!!!!!!!!YAY COOKIE!!!!!!!!!!!!!(I'm hyper ryt now giggle,giggle!)

Ok. here is the look my daughter gives you.
This was at the last team practice.
AND IF YOU DARE TAKE HER QUEEN!

I think I just sit there with my hands on the side of my head, elbows on the table, thumbs behind my ears. If I feel more relaxed I fold my arms on the table and rest my head on my arms. With online chess, I don't necessarily have a chess face but I do lean my chair back with my legs whenever I'm thinking out moves.
I've heard of a poker face, but I've just noticed many people have a chess face. Bobby fischer and many others did. what is yours? mine is both hands on the top of my head, with my elboes on the table. (in a real game not online.)