i find it really varies, but mostly i am worse than you guys

if it is raining and we are home all day then it is probably on quite a bit with dd either watching it or not but if it's sunny and we are out then much much less or none at all. last winter when i was home with both of them and a young baby it was on way more than i wanted it to be. some days this spring or last summer i can honestly say none.
as charlibob does, it tends to be on in the background and dd sort of watches it as she putters around and plays with her toys or looks at books, not sure how much watching she actually does she's a pretty busy kid. it is for sure on while i get ready in the morning 15-20 min. if dd doesn't have a nap we have quiet time and this is usually watching a few shows (she really loves dora), if she does have a nap then i have to wake her up and she's such a bad waker upper that i usually put a show on then too to help the process. and another 30 min at least while i make dinner.
so on average maybe 2 hours but sometimes much less.
for those of you with kids age 2ish sesame street has a good website with some games for young kids. "video games" sort of. they can push the buttons and see elmo singing head and shoulders or twinkle twinkle. dd gets a kick out of it but it's not an independent type of play, she needs help.