TuneIn does have a feature where you can look up particular shows to see when they're playing. However, none of the streaming apps have reminders like you suggested. Nonetheless, TuneIn is a great app for streaming many, many radio stations and webcasters throughout the world.
However, some over-the-air broadcasters have taken their streams off aggregators like TuneIn, in order to incorporate them into their own apps. Clear Channel puts all their stations on their IHeartRadio app, which is very good, IMO. Doesn't have reminders for particular shows, but it does offer continuous streams of certain ones (like local morning shows, talk shows, AT40 and others) for anytime listening.
CBS has recently done the same with their stations, incorporating them, along with Yahoo! Radio, into the radio.com and Yahoo! Radio apps. Unfortunately, these are not good. Very unstable, prone to excessive buffering, and the stream will stop for no reason whatsoever. In addition, CBS is very slow at correcting their mistakes and releasing updates. Since September, the last time they updated, their Android Market page has been flooded with complaints and scathing reviews from users. Considering that CBS owns, of all things, CNET, once the go-to site for downloads and tech news/reviews, this is extremely embarrassing.
In addition, Townsquare Media has their own app, which I believe is called Radio Pup. I know little about it, since Townsquare is a pretty small operator and doesn't really have the content to make a separate streaming app successful.
