I'm fond of TuneIn, a free service that lets you tune in to radio broadcasts from all over the world. I used it last night to listen to Pacific Coast League AAA baseball, and I've previously tuned in hockey games, news stations from far-away places when there's breaking news, and the occasional music channel.
One of the remarkable things about TuneIn is that they have program schedules for the stations they are following, and so you can get real time updates for what's playing now and who's playing whom. The front page rotates new songs that if you're a quick click you can hear more or less in their entirety as they are being broadcast.
A particularly useful part of TuneIn is its "trending" tab, where it gives you real time feedback on which channels have the most activity. When people are listening primarily to music, it's a slow news day; when the top station is an all-news local channel, there's breaking news.
The TuneIn Android app has nearly all of the features of the web site, and it takes advantage of knowing where you are to offer up local stations. In addition there's a "TuneIn Radio Pro", which gives you record and rewind for $4.99. There has to be a monetization strategy in there somewhere; they also serve up ads as you connect to some channels.
Recommended. For public safety scanner monitoring, Broadcastify is a good complement.