While I cannot post every useful and well made app in every post, I'd recommend a search as many users have posted a lot. Here is what I can recommend:
PDF:
GoodReader or PDF Expert or ReaddleDocs
Games:
Angry Birds, Cut the Rope, many more
Office apps:
Pages, Keynote, Numbers
Productivity:
DropBox, Evernote, 2Do: Tasks done in style, LogMeIn Ignition
New:
FlipBoard, CNN, Pulse News
Thats my rec.... this may vary as you may have diff uses for the iPad. Congrats on the purchase.
One of my new favorite apps are HBO Go and Max Go (Cinemax). They're both free on the app store but require a subscription. CNN is also a good app to check up on news.
What do you like to do? I do everything on my iPad. I am a photographer so I do a lot of photo editing with it, I play games watch movies, I am also into art and I do a lot of drawing on my iPad also. Are you into music? Are you into social networking? It all depends on what you like to do. I'm into a lot of creative artistic hobbies so the options are endless with my iPad.
That is sort of like buying a computer and asking us what you can do with it. Everything? We need to know a bit more about you
For me, I mainly use it for reading (GoodReader, iBooks, Kindle) and writing (Evernote, VoodooPad, SimpleNote, Pages). Occasionally, I will use it for watching stuff (Netflix, HuluPlus), but I don't play any games on it.
Yeah, seriously, just think what you can use it for. i use mine to browse through newspapers and magazines. For some reason, I have a much better time going through my iPad for reading than through my laptop. It seems a lot more interactive?? maybe that's not the word, but watevs.
As others have said, it's a tablet computer. Do what you will.