Evernote - just starting to use it though, and hadn't considered the offline issues that someone mentioned above.
PDF Expert - wonderful tool for working with pdfs. I like iAnnotate, too, but so far PDF Expert is scoring slightly higher.
TED Talks - great way to refresh myself during work breaks. So much inspiring stuff on there.
Voice memos - I use this to record supervision meetings, lectures, memos to myself and it's very convenient. I'll probably continue to use just that if Evernote voice memos aren't available offline.
123D Sculpt is just a really fun app if you need some distraction
My local app for checking public transportation. Extremely useful.