I use it for lots of things.
For fun:
Web surfing, reading, forum posting
Facebook
Games sometimes...
Music to my jambox
Photos sometimes
For work (I use it a lot at work, which is why I bought it) -- attorney:
Second window on the code or a case so I can work on the pleadings next to it on the 11" Air
Showing the client a document in court - I have all my client files 100% digital and on my law firm dropbox account, so they can read the doc while I continue working on my laptop in court
I use the mini in court to read my notes when I'm making oral argument before a judge or jury, and I can type on it pretty quick so for short notes ill use the mini. If I need to take serious notes, I whip out the Air cause I used to work as a medical transcriptionist so I can type close to 200 words per minute and get everything that is said word for word.
The mini fits in my suit jacket pocket, so for simple hearings ill roll into court with only the mini in my suit jacket, and literally have my whole law firm there accessible
I send faxes from my mini using metro fax, which can fax directly from dropbox, so that's sweet. I can prep the doc on the laptop, save it, and then fax it right there on the ipad. I also receive faxes and can save them right into the right folder on the mini
I use signeasy to be able to sign documents on the mini. I had a client sign the representation contract yesterday using their finger on the ipad. Very powerful tool here. I could get a doc faxed to me, I can review it and then sign it and fax it right back all on the mini
Of course I can do all the same on my iPhone 5 64, were I to have to. Essentially I could bust into court with just my cell phone and still have everything I need.
The iPhone dictation button and the mini dictation button makes it easy to dictate notes into the client case notes word document
I use documents to go on both the iPhone and mini because it syncs well with dropbox
Photobucket is good too
I use scanning software on the mini and iPhone to take documents and make them PDF when I'm away from my main scanner in my office...
I could go on, but I think I got the idea across.
The ipad mini is this litigator's dream tool!