Generally, an hour or two and then I take a break.
Per day, though, it's probably more like 4-6 on days when I don't work or go to school.
Still this, though on the weekdays that has shortened to about thirty minutes, maybe an hour. The "varies wildly" answer might probably be the best one these days, anyway.
EDIT: On the weekends, that's not "4-6 hours at a time". That's more like 1-2 hour sessions enough times in the day to add up to 4-6 hours, so like 2 in the morning and 2 in the late afternoon or something. Seems like a noteworthy enough distinction to me.
It varies. Generally I will play for less than an hour at a time. Sometimes I will just fire up something like VVVVVV and I'll play for less than 5 minutes and that's me done for the day.
Sometimes I really get into a game and I will play it for 5+ hours. I've played Skyrim all day for a week before.
I cram 4-5 hours two to three times a week. I don't get a lot of time to play games during the weekdays as my GF generally hogs the big TV weeknights, so I usually get my gaming in early Saturday and Sunday morning before we head out and once every two weeks I have a day off from work where, if I have a good game on the go I'll play for 8 or so with a break in the middle for cleaning up/lunch.
My AVERAGE session is usually just one or two online ranked games of NBA 2Kx, but when I'm playing a story-based game I can find a reason to get invested in that session can easily stretch 5-10 hours. GTA V was three 10-15 hour days in a row for example, Tomb Raider was four 3-4 hour days spread across a week, Last of Us was a pair of 9 hour sessions back-to-back, Bioshock Infinite was two five hour sessions, and so on.
I'm a huge proponent of binging on entertainment, though. My favorite TV shows these days tend to be shows I get into late in the game (Community, Breaking Bad, Parks & Rec, etc.) and have a huge back catalog I can obsessively digest; it also helps with keeping the weird condensing of time going on with a show like BB which is a little under a year spread over 5 seasons and 6 or 7 years of production.
On the weekends, when I'm not busy or the fiancee isn't around I can play for 5-8 hours depending on how much time I have. Regularly 1-3 hours during the week after she's in bed.
At work when I'm not too busy though I can usually get in tons of time. When I'm printing as all I do is sit and watch the press for 8-12 hours. It's the reason I got a Vita and a 3DS.
Between 1 and 2 hours. But if I really love a game, Mass Effect, Skyrim, Fallout 3, I will play for 3-4 hours, maybe more if I have nothing else to do and I am really into it. The first Mass Effect was much like this. I ended up playing from around 7-8 at night to 1 in the morning, and I had to get up at 7 am for work. :)
Nowadays 1-2 hours if I'm really lucky. Having a kid really cuts down the time and when he finally goes down to sleep I'm too tired to play much longer (typically). Occasionally I will brute force endings of games regardless of tiredness (see Tomb Raider last weekend, Dust a month ago) but I usually try not to go to crazy with gaming sessions.
EDIT: When I was single it was easily 4 hour average, used to play 8 hours straight of Rock Band pretty much everyday (by myself even, man I miss music games).