How can I browse WWDC session videos directly on my iOS device or AppleTV? On my Mac, I can log in to the developer center to watch the videos from the website, and that I can log in on iTunes on my Mac to browse and download them. However, is there a way to browse and watch WWDC session videos directly from my iPad or AppleTV?

I've tried logging in to the Apple developer center on my iPad's browser, then viewing the videos "in iTunes"--this brings up the iTunes app, with a section called "Developer on iTunes", but also a pop-up dialog telling me "Access Denied". On the AppleTV, there isn't even a browser, and searching iTunes U in both places has yielded nothing.
You can find them in iTunes U, and if you log in at 

Apple Developer Site

with a valid developer ID, you will get a list of videos - and there is a button to "View all in iTunes".

When I did this a minute ago on the iPad I got a "One moment please" followed by a redirect to iTunes, and all the videos appeared in categories, all marked "Free".

If it isn't working for you then there must be a problem with your account. If you can access it through the Mac you're probably going to need to talk to Apple about it. 

You've probably thought to try "Clear Cookies and Data" from Preferences->Safari?