Free Launch can run all of my apps directly from the iPad desktop. It has 160 launch buttons on four pages!
Listful is a very handy list maker. I use it to create shopping lists and to-do lists. It can sync between devices.
Radio Star is my companion in the car. It is an automated radio station that plays my favorite tunes via Bluetooth
CalcWiz is a handy calculator. It keeps a log of all calculations that I can then copy and print.
WeatherScope connects to a service called Apixu and downloads 10-day forecasts for my ten favorite locations.
Syntil8 is a miniature synth with keyboard that can play any of 127 MIDI instruments polyphonically.