Right I'm a teacher so what apps are good for work?
Pages, to start with, for basic word processing and page layout. I use this for all my class handouts, assignments, correspondence, et al.
iCab is a better browser than Safari. Both are built on WebKit, but iCab has tabs, file downloading (and limited uploading), rapid in-page navigation, and many other features to speed up online research and the like.
Dropbox.
Articles is a nice front end for Wikipedia.
iBooks -- not so much for the bookstore as for use as a general .PDF and .epub reading and organizing tool. Goodreader is also pretty awesome, though with so many features that it takes a bit of time to learn.
There are a gazillion notebook or note-taking apps. Everyone has their faves. I like Chapters, IAWriter, VoodooPad and SimpleNote, each of which has some unique quirky advantage over the others.
I am not an organized person but daughter swears by a pricey organizer/ planner app called Things, and also likes iStudiez Pro.
Have fun!