I usually do, but sometimes it's easier not to.
Besides, what's the point? If it's supposed to keep me from seeing things I shouldn't see, it doesn't do a very good job of it. I can easily lie, and if I find I haven't entered the right age, it's trivial to try again. As a user, I just find these a hindrance, especially when I'm forced to fill them in multiple times as I navigate from page to page.
Bad Company 2's website is at least a bit better than most: rather than ask for your date of birth, just enter your age. 3 key presses and you're done. Sure, it's still pointless, but it's a lot better than navigating through a bunch of large drop-down menus.
Seriously, we have to stop expecting companies to act as parents. It shouldn't be up to EA or GameTrailers to keep kids away from things their parents wouldn't approve of -- it's completely out of their control. They can't tell a kid's age, nor do they have a clue what their parents would find acceptable. Let parents be parents and supervise their children. Better yet, let kids do what they always do and find out what real life is like for themselves. Parents never successfully kept their kids from drinking, having sex, and staying out late at night no matter how hard they tried. We all learned the same way and most of us came out alright.
I would love a Firefox plugin to skip age gates.