I don't have a solution for a native app. Wish there was one. Orb works but its a pain to either keep your computer on or set up Wake on LAN on your router.
The easier solution is Moodio FM. Moodio FM does not provide any content. All they do is simply convert internet radio streams to formats that are suitable for mobile phones.
On your desktop computer, go to
Welcome to Moodio! | Moodio Set up a free account. Search for the station you want to listen to. Most popular stations are already on there. If you find your station, save it as a favorite. If you don't find your station, and you know the station's stream url, Find "add a new station" from the main Moodio page to enter the stream url. The instructions on how to find a stream url are also on that page.
http://www.moodio.fm/new_station
So, once you have all your favorite stations saved to My Stations, you go to the Moodio FM mobile site on your phone.
m.moodio.fm
Log in with the info from the moodio fm account you just created and you'll see your My Stations list. Note, you cannot add favorites to My Stations from the mobile site, so make sure to do it on your desktop.
Click the link for one of your stations and you should be playing the station in a few moments. For me the stream comes over the native Android Video player, which is odd, but hey it works. If it's not working for you, you might need to download the free version of either StreamFurious or DroidLive from Android Market to make it work, but it will work.
Good Luck