I just got a Kindle Fire and I'm only scratching the surface of what (besides reading books/watching video) to do with it too. It's nowhere near as capable as my laptop BUT it also fits into a jacket pocket so I've been carrying it everywhere instead of making the decision "lug around laptop bag/leave the damn thing at home". So far I picked up a ton of free apps to see what's useful. What I've been using the most:
Wi-Fi Analyzer - Find open wi-fi (it lists the open ones with an *, handy)
Bloomberg - quick look at financial news while I'm in a bar/restaurant
Engadget - gadget news ditto
newshog - ditto other news
WSJ live - Wall Street Journal news videos
Opentable/Urbanspoon - find bars/restaurants
Fandango - movie theater times
Pandora - listen to my Pandora channels
ebay
Mapquest - maps. I'm working on getting Google maps working (it's a bit of a hassle on the Fire)
Weather Channel/Weatherbug
USTV free - sometimes gets HBO/Showtime/Starz movie channels, news stations
ES Task Manager/GSam Battery Monitor/AppSwipe - find out what's running and slowing down my stuff, lots of stuff doesn't stop the app when I leave the screen, kind of annoying esp if it has audio.
The built in browser mainly to look up addresses and phone numbers.
I also have Amazon Prime so I have been watching a lot of the free streaming videos - Dr Who, Red Dwarf, a bunch of noir films. Mostly I have a bunch of books and jazz/classical music downloaded so I have something to read/listen to while stuck waiting somewhere with no wi-fi.
I'm working on getting it working as an additional display screen for the desktop/laptop - it's handy to keep a man page displayed without needing to switch back and forth, for one thing. Or to keep displaying stuff I'm monitoring without taking up main-screen real estate.
I couldn't stand the tiny display on the earlier smartphones (I have been getting tempted by the later models, but I still balk at the cost of phone + service here), this is a pretty good compromise in being portable but usefully big. Although now I kinda want to try a 10" model, maybe TF700 yum...