Radio Alarm is a powerful iPhone alarm and internet radio player combo that looks good and is stable enough to be trustworthy as an alarm clock app.
multitasking for all features including radio, sleep timer, alarm, etc. (iOS4 and up)
alarm (set various alarm sounds including iPod MP3, radio, sounds of nature, recorded file, shake to turn off the alarm, support for multiple alarms, sensitive snooze time interval, alarm sound with vibration, set 'Fade In/Fade Out' time, set number of 'Shakes')
Radio (listen to 35,000 stations from around the world, antique-style theme provided. - Add favorite stations, search for stations by keyword, enter custom URLs, each country stations)
Sleep timer (sleep timer can be set with MP3, radio, sounds of nature, set 'Fade In/Fade Out' time).