I find Pandora sort of annoying. It seems to hit on a lot of songs I don't really like, and because you are limited to both thumbs-downing AND skipping songs to just a few per length-of-time-they-don't-specify, I end up having to listen to a bunch of songs I really dislike for far longer than I think is reasonable.
I ran into this issue when I was looking for Christmas music that didn't make me feel stabby back in December (the local radio stations that play it play most horrible renditions of songs I don't even like that much to begin with). I set up a station that seemed promising (in that I liked the first few), faithfully marked "like" or "dislike" for each song, and quickly found myself having to listen to songs that made me feel stabby because I'd used up my skips on songs that I only mildly disliked. And it seemed like at least every other song was one that I seriously could not stand. I think I disliked 3 or 4 separate renditions of "Santa Claus is Coming to Town" and still kept getting different artists versions of that song. Particularly for stuff like that, I kind of wish there was a way to specify that I dislike the song itself (but not the artist), the artist (but not the song) or both.
Even from artists I otherwise love, there are a few of their songs that just grate on my last nerve. And there are some artists that I can't stand who apparently lots of other people think are similar to ones I love.
I tried out IHeartRadio on a whim this morning, and seemed to do better with that one. Maybe I just trust DJs to pick out a good mix of songs I'm likely to enjoy based on a brief description than I am to trust what amounts to crowdsourcing.