Sky Guide.
I bought this to help me look at the stars at night. It's pretty spectacular. You can look around in your house, then walk outside to see the real thing. You have to see it to believe it.
Tonight, I went out to look at the ISS going overhead and was flabbergasted to see it also racing across my Sky Guide screen. Turns out, Sky Guide has a $2 add-on that you can add that identifies all the satellites in the sky - I hadn't paid for this add-in, which is why is says "satellite" instead of ISS in the screenshot below. By "satellites", they mean the ISS, jettisoned space debris, Iridium and other comm satellites. Click on one of them for more information about the thing than you care to know. E.g., I just learned, after clicking on an Iridium satellite, that a new set of 77 Iridium satellites will be launched starting this year to significantly improve space-based satellite phone quality. I thought it was dead.
You can zoom in the normal 2-finger way, look "through the earth", search for stuff (e.g., click the magnifying glass, type in big dipper, and you'll see an arrow appear on the screen; just keeping turning, following the arrow, and bam there's your object). It also will give you notifications when astronomical events are going to happen (don't miss the next ISS passing or asteroid).
Very cool. Search and buy Sky Guide. I did not compare this to any other apps, but I saw my brother in California using it and bought.
