I don't know of any plugins, but there's several bits of code out there that do this. If you have access to Flash, you can get a piece of Flash code that will do exactly this. But there's also Real Players, Quicktime...all kinds of things that'll do this for you. You just need a little snippet of code.
I *will* say though, that you should provide an "Off" button if you *really* plan on doing this. Believe me, NOTHING will make a person leave faster than having to listen to something they don't want to, and no way to shut it off.
And, personally, I tend to have my iTunes playing in the background when I'm on my computer - many things that do what you want to do will cut off my music to play yours. I *hate* that.
So, annoying, yes, it is muchly so. But people do it anyway - and that's how you can do it. Just do a google search for a Flash mp3 player (I can't remember that Flash site - there's a big one out there that has all of these scripts already done - you just download and install - flashtips.com, I think? I can't remember... - but it has one where all you have to do is put it on your server, and use a plain text file to call in whatever song you want to play - no editing of the Flash code needed) - you'll find it :)