I love Tasker. If you want to make full use of it it can be a bit intensive to learn but anyone can figure out the basics. It is an app that allows you to have your phone do certain things based on things like your location, what network you are connected to, your location, and other prompts.
Mine is set to silence my phone at work and at the movie theatre I go to. I’ve also set it to require a password for my phone when I am anywhere but home. At home I just turn on the phone and it is ready to go. When connected to the bluetooth in my car google maps navigation opens automatically and when I plug in headphones it asks if I am listening to music or watching a movie and opens the correct app based on my answer.
It really is a fun app to play with and find new things that you can automate on your device.
gReader - RSS reader, simple/intuitive interface but also pretty fully featured; note that since Google shut down their Reader service you have to also pick one of the other RSS services to sign up with, and they all have their own apps too, I just was used to (and already liked) gReader
TweetCaster Pro - Twitter app, which I use pretty much exclusively for following/reading rather than posting
IMDb - app is better than the mobile website, both for looking up movie times easily and for answering when my wife asks what other movies that guy has been in
Kindle - self explanatory
WatchESPN - if you have a cable subscription, you can watch pretty much anything on any of the ESPN networks from anywhere
Yahoo! Fantasy Sports - if you’re into fantasy sports, easily modify your lineups and check your stats from anywhere; I’m sure ESPN has a similar app
Bank apps - both of my main banks (USAA and Navy Federal) have pretty good apps, and I’m sure your bank does too
Mobile Authenticator - if you play any of the Blizzard games or any MMOs or similar, you can (and should) use your smartphone for two-factor authentication
Random utility stuff: a good weather app (I use AccuWeather), a better-than-default calculator, a notepad, a stopwatch/timer, a few different music service apps, a bunch of games but those are YMMV depending on what you like and what you’re willing to pay for mobile games
I have two, MobiCalc Free, which is a progressive calculator - the answer appears as you enter the equation. I just like everything about how this app works.
I also have a programmable calculator, called just that, I think. My only complaint is that it’s got a very clumsy layout (page after page of identical square buttons), and that there’s no way to “lock” a program… mis-taps while trying to either use or create new programs overwrites existing ones far too easily. I have one probability program that takes five careful minutes to enter… and I’ve lost track of how many times I’ve accidentally cleared it. The Eastern-European author hasn’t acknowledged any of my comments, but it’s still the most powerful and capable one I’ve found.
I’d also like to thank mentions of the direct radar-weather apps. I use Weatherbug, but it takes several taps and a noticeable update time to get a current weather pattern. Here in the “wait fifteen minutes” weather zone, I depend on the satellite and radar more than anything else. Having an app that instantly pops up full-screen with the radar imaging is really nice.
Soundhound, Shazam, or something of the sort. Basically, if you hear a neat song, or you hear a song that you just can’t seem to remember who performs it, fire up the app. It’ll listen to the song, tell you who performs it, and (with Soundhound at least, I don’t have Shazam) even show you real-time lyrics and give you a link to buy the song.
A couple that I’ve found useful are FlightBoard and FlightTrack. You can look up arrivals and departures for every airport in the world with FlightBoard, and FlightTrack allows you to track specific planes in the air. Doesn’t sound like much, but awesome when you need the info.
One that I love, but requires a rooted phone: Root Call Blocker. It allows you to set up blacklists of calls to block, lets you pick the behavior the blocked caller gets (a quick rejection? answer and hang up? just ring and ring forever? straight to voicemail?), and even lets you use wildcards if you get nuisance calls from similar numbers. You could block a whole area code if you wanted to. Alternately, you can block everyone, and only let calls on your whitelist get through. Great app.
If you are an older engineer like me you can download Droid48. It is an emulator of the HP48G graphing calculator. Once you go RPN you can’t go back to normal calculators.
Google Sky Map is more fun than any game. It works off your phones GPS position and gives a view of the stars, planets and all other astronomical objects in the sky at the time (with names etc). When you move the phone around, it changes the view according to where the phone is pointing.
I’ve been letting Dan Carlin’s recent episodes on WWI run while I sleep and it’s been giving me some very disturbing dreams as he tends to focus on the horror and the macabre,