Developer: AOL Inc.
Price: free Download on the App Store
If there was no competition, I would be tempted to recommend AOL Radio, the free internet Radio compilation app from America On Line. The app has one huge thing going for it — the price (Free). But its hardly the best Internet radio app out there.
Like other Internet Radio Apps, AOL Radio is organized by genre. There are most of the top level standard genres (Alternative, Country etc..) but there are no deep sub-genres, and the number stations within each genre is limited. Choose "Blues", for instance, and there are exactly 5 choices, none of which are very appealing. While the app claims "200 Radio Stations", some of these stations are really just random compilations of AOL — for example "All Radiohead".
One original aspect of the app is the "Nearby" tab which uses your GPS location to pull up radio stations near you. Tuner Internet Radio, for instance, doesn't have this feature.
Overall, Pandora and LastFM are both superior for overall music discovery and general personalized music. Tuner Internet Radio is a better choice for actual Internet radio, but it will set you back 5 dollars.