Not aviation, but I'd recommend the following.
Appbox
BatteryDoctor
Camscanner+
Dragon Dictation
Dropbox
Kindle for iPhone
Flight Status
Informant
Shazam
Skype (for calls when abroad)
Sky+ (if you have Sky it lets you set up recordings at home on the fly)
Spotify
Stanza
TrainTimes
Weatherpro (in addition to Aeroweather)
WunderRadio