Sure, I've done it playing Pokemon before. It's especially easy to nod off with a handheld because there's more room to get comfortable, whereas you usually need to sit up and stare at the TV when you're playing on a console. Just got a new, plush couch, too, so I'm willing to bet Pokemon won't be the only game that gets the sleepy-time treatment in the future...
I've done it as well. Often it's because I'm tired that day to begin with, though it probably doesn't help that if I'm playing at home, I'm typically flopped across my bed to play. It probably depends on how interactive the game is as well. I think I'm definitely more likely to doze off to something like a visual novel or a cut scene than to an intense boss fight.
Very true! It's usually a cut scene or slower paced game when I doze off also. I'm also laying on the bed or sitting on the comfortable couch when it happens plus I'm already tired from a long day. I guess I should either drink a bunch of coffee or get well rested before playing. Coffee I choose you!
I don't think I've actually fallen asleep while playing a 3DS game, but I've definitely nodded off before, like when I'm playing a slow-paced game with calm, casual music, such as a Harvest Moon game. Especially after a long day and I'm in/on my bed or something. XD