iPhone and iPad Apps
Mobile Learn - If you're on a campus that uses blackboard, and you suddenly realize that you meant to announce that the reading assignment for next week has changed while walking across campus, then you will love this iPhone interface to blackboard.
Star Walk - sky charts that take advantage of GPS + accelerometers to align with the actual sky you point the phone at (useful for convincing people you actually do know the constellations...)
Planets - locations & rise/set times for solar system objects.
HubbleSite - the official HST pretty pictures app.
VelaClock - sun & moon rise/set times, astronomical & civil twilight times, etc.
CosmoCalc - cosmological distance calculator. Set a reference cosmology and redshift, and CosmoCalc will calculate astronomical distances and scales.
GravLens -simulate the effect of a gravitational lens
Transient Events - Download events which meet criteria from the Skyalert database. See a RA, dec, finder chart, reference image, and the discovery images.
Exoplanet - database of known exoplanets with ability to plot various property correlation diagrams, links to exoplanet news (mostly paper press releases), and a fairly slick 3D milky way model showing the locations of all known planets.
arXiv - an app to access abstracts and papers on arXiv. It's a great way to check new submissions when commuting on a bus.
Brown Dwarf Converter - an app to convert between brown dwarf spectral types+age and masses.