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TuneIn is what most people use for streaming radio on their iPads. It's $2.99 and comes with 40,000 radio stations. One cool feature about this app is that it lets you pause and rewind the live radio streams (just like DVR). If you're looking for a specific station, you can search their full list of radio stations here.
ooTunes is similar, but instead of just pausing and rewinding the songs like TuneIn does, it lets you actually record the songs to your iPad. It's a little pricier at $4.99, but it'll come in handy if you're somewhere w/o internet or just want to save a song you like. This app also shows the lyrics of popular songs so you can sing along. It has a pretty comprehensive database of radio stations similar to TuneIn. You can see their full list of stations here if you're curious. It also streams Sirius if you have a subscription.
Get Radio.com and you won't need your Sirius subscription anymore . What sets it apart is that it's owned by CBS, so you'll get access to high quality radio stations similar to Sirius such as KROQ, Live105, 1010 WINS, AMP radio, ESPN sports, CBS news etc. Their stations are conveniently divided into music, news, and sports, and there's a map so you can listen to your local stations. What I personally like about Radio.com is that it's US-specific, which is nice for anyone who doesn't want to sift through 10,000 stations all over the world that aren't in English.
I use TuneMark, it's got all the stations from around the world. And it's only $1.
My favorite app for listening to radio stations is PocketTunes. It has a large library of free stations and lets you record live radio too. You can filter stations by country and genre. You can play certain stations in the background while other apps are running, but for those that can't, there's a built in browse so you can stay in the app while surfing/checking email. You can also access the Sirius stations if you're a paid subscriber.
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