I recently spent some time in the Apple App Store to see what was available for astronomy and after looking through over 500 applications and downloading / reviewing about 75 of them (most of them free), I have distilled things down to a fairly short list of applications I found informative, inspiring, useful, easy to use, or just plain fun. If you know of other great apps, I encourage you add to this list. I have listed only a few apps that cost more than a few bucks for obvious reasons. There are several more apps out there that cost quite a bit; however, I have elected to not post any information about the more expensive well known apps. I also don't intend this to be, in any way, a complete listing of apps available.
Note: If you don't like Apple products, I encourage you to post your own version of this list for your favorite device. Enjoy!
Scope Nights: Astronomy Weather Reports - $2.99
Great little app that breaks down the weather forecast specifically for observers. You can even customize some of the app features to show good or bad conditions based on what you are willing to put up with. One drawback is that the app refreshes every time it is pulled up vs. on demand or at a lesser interval.
myCSC - Free!
Carry your favorite Clear Sky Charts (CSC) in your pocket! Amateur astronomers in North America monitor local sky conditions using the CSC web sites which provide a very detailed 48 hour color coded observing forecast chart for cloud cover, transparency, seeing and other factors. This app contains a database of more than 4000 forecast.
Next best thing to going to the website and pulling up your CSC and you get to see your 3 favorite charts at a glance.
Sky Harbinger -Free!
If you like a screen full of data, this is your application. This app automatically detects your location and pulls in the forecast with the following parameters for the next 72 hrs: Cloud cover, Seeing, Trans, Temp, RH, DP, Precip., Wind, and Moon%. Some features of the app cause a server time out, but still worth having since its FREE.
Redshift - Astronomy - $11.99
Worth every penny. Just check it out, if you are looking for it, it's probably in the app. (app tracks the sky)
Star Walk - $2.99
Budget version of Redshift, but still an amazing product with over 6 million downloads. Hope the publisher is enjoying his/her early retirement. I really really like the "skylive" feature, it allows one to quickly run thru rise set times and illumination phase data on the fly. Go get it! (app tracks the sky)
Solar Walk - $2.99
Our solar system at your finger tips. Eye candy for when you have nothing better to do than indulge yourself in your favorite pastime (in day light or on a cloudy night of course

Moon Globe - Free!
I am getting started on the Astronomical League's Lunar Observation program, and I decided to grab this one. You can't do better for free I'd bet. You can search the index within the app to locate specific features, spin the moon as if you are God, and you can change perspective and lighting at will to see how it affects various features. Great App!
ISS Visibility - $1.99
I use this app all the time. I especially like the ground plot feature. It really helps the user figure out where to look for the ISS without having to do mental gymnastics. I like to take screen shots and share sighting opportunities with friends and family. Its also fun when someone asks if they can see the ISS tonight; I just pull out the app, hit the refresh button and give the answer. Fun factor = high; especially when the ISS is actually going to fly by or is that bright object flying by.
Meteor Shower Calendar - Free!
Ever witnessed a meteorite streaking by and wondered if there was an active shower? This app will tell you.
Comet - Comet Ephemerides - Free!
With Comet ISON looming large I decided to check this one out. Shows a list of known comets and can be sorted with various parameters. Useful and informative. Why not? Its FREE.
Glossary of Astronomical Terms - $1.99
Need I say more?
Soho Viewer - Free!
Like the sun? Want to see the latest imagery from the Solar and Heliospheric Observatory (SoHO)? Get it! Also check out i3DSun or 3D Sun- Free!
APOD Viewer - Free!
Like to pull up the Astronomy Picture Of the Day and read tid bits about the universe?; grab this app. Think great wall paper for your iPhone or iPad.
Cosmic Universe - Free!
Just like one of those science shows that talks about the structure of the universe and showed you one of those amazing 3D views of the cosmos; however, you are in control. Get this freebie and have a look around. It tracks the sky with an overlay of the galactic super clusters, gasses, and dark matter. Total eye candy.
PTT Universe - Free!
Description: Access a universe of knowledge about the Universe with the Portal to the Universe app! Designed in a magazine style, this free app brings the latest scientific breakthroughs gathered from hundreds of news and blog sources every day. It’s never been easier to be well informed about the latest space news.
So far this app has delivered.
New General Catalogue (NGC) List - Free!
A simple interface app that can help ID what a particular NGC is; though not a complete list, it could be useful in a pinch.
Again, please feel free to expand this list with your favorites.
-Bill