under the assumption that something like "reading a book" is considered productive
1) surfing the web from my couch
2) some games like plants vs. zombies are sublime on a tablet, much better than on a pc imho
3) pdfs read much better than on a pc or a kindle
4) comic books (cbz and cbr files) on a ~10" tablet are almost as good as the real thing
5) when docked, my tablet makes a fantastic picture frame showing the photos in my google+ account
6) there's some music production software that are really quite good, I like Caustic myself, there's similar for iOS.
7) lots and lots and lots of pretty decent painting apps
8) I use it to see notifications, task, etc. things that I've entered from my PC into some "cloud" service. calendars, trello tasks, etc. Just bringing my tablet into a meeting with trello pulled up on it makes it seem like a have a super human memory and is far less intrusive than a laptop
9) use it as a third monitor, there's some great wifi streaming apps that tell your OS to use it as another monitor. Sure it's a bit slow, but if I stash my email program over there, or a shell that's tailing a log or something, it's perfectly adequate
10) better yet, just put a shell app on there direct and ssh into the server and tail the app that way, keeping tabs on a long running startup process while I'm in the bathroom has never been easier
11) remote to my PC running VLC...it's awesome for this, I can seek fast forward and rewind, control volume, pause play, whatever...custom home touch panel remotes don't hold a candle to this
things I don't do
try to type non-trivial amounts of text quickly without a keyboard, which is where most of the examples from this post are about, which is weird since he's using a transformer prime...who's entire point is the keyboard dock