Some apps I've tried:
Sports and Navigation
Runkeeper: Great app for tracking where you go and how long it takes you. Dunno about the calorie counter, but the basic features seem excellent. Trifle pricey.
GPS Drive: I'm loving this application. $2.99 a month or $29 a year for voice GPS, and it seems to do a pretty good job to me. Easy to use.
AroundMe: Love this app -- you're somewhere driving around and you need a restaurant, or gas, or whatever. Boom!
ArcGIS: There's a lot in this app. Little slow, but the topo maps alone are worth it.
Yelp: Sort of like AroundMe, also good.
Spyglass: kind of a neat navigation/photo logging tool, but I'm not yet sure how to use it or where
News
I have WTNH.com, Discovery, NYTimes, and NPR News. All pretty handy. The WTNH app is pretty handy actually. I like the Discovery app for easy quick science and archaeology news.
Museums
I'm a museum guy, and have apps for the Louvre, AMNH, Smithsonian, and Cluny. The Louvre app is really great, as is the AMNH app, especially if you're actually there. The AMNH also puts out a Dinosaur app, which is kind of neat. The Smithsonian has a MEandertal app, which converts a picture of you into a Neandertal or Homo Heidelbergensis rendering. Kind of fun -- great for Facebook profiles. The Cluny app is French, and pretty clunky, but has some neat medieval material. I think they're all free or low cost.
I'm still trying to find a decent, simple, cheap, list making type app. I have Bento, which is sort of FileMaker for the iphone, and ListMonger. Bento is more than I want to handle simple lists ("places to eat in NYC" with a sub-list of places I can check off), and ListMonger is okay but not great.