My iPad keeps asking me for my iTunes account password
Solution 1:
Try a reset - hold the home and power buttons down until the apple logo appears.
I had a similar problem when I'd downloaded an app update, but lost wifi, and it got caught in a loop, and the reset seemed to resolve it.
Solution 2:
If a reset like Jaydles suggested doesn't work, syncing it to a computer with iTunes that has been registered with your account will resolve the issue.