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Everything and anything.

Asking that is like walking up to the Genius Bar and saying 'it doesn't work' and nothing else.

If you have so little clue what you want to do with it perhaps you shouldn't have bought it. But since you did start by looking at the featured and top apps and try a few freebies. Then work your way out from there.

And don't forget to keep an eye on what might be free on the music etc side.
 
I have a mini and here is my favorite free apps, they might not still be free but recommended.

1. painting: sketchbook express and inkpad
2. presentations: flowboard
3. project planner: project reno (iphone app but works good)
4. offline reader for webpages/youtube: Pocket
5. remote picture viewer from pc: airphoto
6. radio: tunein
7. picture editor: snapseed and photomagic
8. Free recommended apps: apps gone free
9. Games: pinball hd and reaper-tale of a pale swordsman
10, wifi file-transfer: feem
11. file transfer/sharing internet: dropbox
 
My favorites (other than productivity apps like numbers and google drive):

Magical weather
Digits calculator
Converter (units)
Credit Karma
Tapatalk HD (when they fix the crashing)
 
It all depends on what you want to use it for. Apps are exactly the same as the ones for the larger iPad. Just think about what you wanna do and start downloading. The ones I use the most are these:

Google Quickoffice
Kindle
Mail
Microsoft OneNote
Skype
YouTube
 
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