I've been listening to Pandora a lot lately. I have a bunch of stations defined, in varying degrees of bakedness, plus a few stations defined by other people. But what I do most of all is use Pandora's “Quickmix” feature, which allows one to select some or all of one's defined stations; Pandora then cycles among them randomly, a song at a time. So I get an eclectic and unpredictable station when I want it, and a more targeted station when I want that.
If you have any interest in what I'm listening to, you too can ride along on Froomkin's Pandora 'Quickmix'.
As I understand it, the way this works is that what you get will be determined by the same algorithm as determines what I get, but it won't necessarily be the identical songs. Plus, I get to alter which of my stations are in the mix on a rolling basis (and I do!), and also to modify my stations, also on a rolling basis. When I do either of those things, that changes the algorithm which determines what you hear.
But, as I understand it, you don't get to change what I or others hear. All you can do is stop listening, mark a given song as something you don't want to hear again for a month, or (up to six times per hour), skip to the next song.
At this writing I have it set for a fairly broad mix, which includes a little folk, a little comedy, a little weirdness, some great solo singers (mostly female but including Leonard Cohen) and quite a lot of 80/90s pop and especially (then) alternate rock. I find I can't work to rap, so that's out of the mix, yes even Gil Scott-Heron, except sometimes on the weekend.