Just like crying every time you left her to use the restroom, just like she used to eat 14 times a day...this too will pass:)
We were formerly a "no tv" household, and have morphed into a "Dora" household. She's just over 2 now and has a repertoire that I give into on rainy days or days I'm just too tired to fight. Dora drives me insane, so I Tivo other things for her and give her other "good" options. This has led us to trying Backyardigans (good for a few weeks), Diego (he's the Dora "backup"), Little Einsteins (the whole family likes this one!), Dragon Tales (she has started to chant for that one this week), WordWorld, Sesame Street, Tigger & Pooh and Mickey Mouse. A regular day is one 1/2 hour before we leave the house for playgroup/errands and one before bed, but like I said, rainy/cold days or days that I'm dragging it, it might creep up to a total of 2 hours. But that's it. Beyond that, turn it off (or put on "boring tv" - Food network, HGTV) and they'll find something else to do.
Hey, have you tried timeouts? As in "if you ask one more time for Caillou, you'll be in timeout?" I'd give 2 or 3 warnings then follow through.