These smartphone apps do radio — in one way or another — and blur the lines among traditional broadcasting, on-demand service, and customized personal “stations” that play stuff that’s like what you like.

Stitcher Radio by Stitcher Inc., a free app for Apple, BlackBerry, and your desktop PC, plays live and on-demand talk radio and podcast segments. The name implies you get to “stitch” together your favorite programming for listening anytime.

Listen to multiple segments of a program, such as “This American Life” from Chicago Public Radio or “Old Time Radio Dramas.”

It’s mostly free, though a list of paid subscriptions to other talkers’ podcasts — Rush Limbaugh and Don Imus, for example — is easily available.

TuneIn Radio Pro, at 99 cents for multiple platforms by Synsion Radio Technologies, is a tuner for AM and FM broadcast radio from around the world, including the newer digital HD broadcasts. It claims access to 50,000 stations.

Pandora Radio, free for multiple devices by Pandora Media Inc., is the gold standard in custom music radio. Start by selecting a genre of music, or by typing in the name of an artist, song, or composer.

Slacker Radio by Slacker Inc., free for multiple platforms, is like Pandora but claims “four times the music of the leading competitor.” It offers several options for fine-tuning of music selections, recording for off-line play, and the opportunity to edit your earlier ratings.

HiDef Radio, by Smartest Apple, is free and boasts that it plays Howard Stern’s satellite radio show on Apple devices without a subscription. Promotional material says the app pulls in 30,000 stations, but in the app they’re called “feeds.” You can add any streamed station through the search screen.

For sleepless newsies, a companion app, 5-0 Radio, plays police scanners. A paid version, HiDef Radio Pro, for $1.99, lets you record feeds and send them via e-mail.