So the iPhone and iPod touch lack an FM tuner. So what? AOL Radio fills the gap and then some, serving up some 350 stations of streaming-radio goodness. It’s a fantastic app for music and talk-radio fans, and it doesn’t cost a penny.

When you first run AOL Radio, you’re presented with a list of categories, starting with AOL Recommends, What’s New, and Spinner.com (a collection of about 17 themed stations from the site). From there the list spans 25 genres, from Alternative to World/International. A few taps is all it takes to start listening.

You can also tap the Locals button at the bottom of the screen to find stations in your area and across the country. The app can automatically find nearby stations based on your location, a nice touch.

Most of the AOL stations display both album art and song info. While listening, tap the accompanying magnifying glass to access three handy options: Find on iTunes, which takes you straight to the iTunes Store so you can buy the song (if available); Find on AOL Music, which runs a fairly useless Web search; and Remember This Song, which adds the current tune to the app’s Favorites list. Speaking of which, you can also add individual stations to Favorites—great for quickly returning to preferred stations later on. Want to retrace your listening steps? AOL Radio maintains a list of recently played stations and songs—another genuinely useful feature.

We tested AOL Radio over Wi-Fi on an iPod touch and it performed flawlessly: We didn’t hear a single hiccup in the playback, regardless of whether we played AOL or local stations. It stands to reason that 3G performance should be similar, though many iTunes reviewers have cited problems with EDGE connections. Of course, because AOL Radio is free, you have nothing to lose by trying it.

We have exactly two complaints with the app. First, we couldn’t find any NPR stations, probably due to licensing issues. Second, you can’t leave AOL Radio running in the background—the music cuts out the moment you exit the program. Those are disappointments, to be sure, but they don’t diminish the overall appeal of this incredible freebie.