There are a number of options for listening to Internet radio over a Wi-Fi connection on an iPod touch, including iTunes Radio, iHeartRadio, Pandora and Spotify. Many of these options have upgrades which may be purchased to listen to radio without ads.
All iPod touch devices come with the free iTunes Radio feature. This feature is within the Music app on Apple devices. iTunes Radio is free and allows users to create stations based on genres, artists or songs.
If someone is looking to stream FM or AM radio stations on an Apple device, the free iHeartRadio app allows users to listen live to various public radio stations from around the country.
There are other Internet radio services, such as Pandora and Spotify, that offer free apps through the iTunes store. Both services offer free versions as well as premium subscriptions for a fee.