In Lord of the Rings Online, by Turbine Games, you can play a minstrel. Your minstrel, or any other character class for that matter, can play a musical instrument while you're not out beating the crap out of Sauron. It's a matter of using the number keys like a keyboard, along with the alt and control keys to shift up or down an octave. Essentially, if you're a keyboard virtuoso, then you can play just about anything.
But that's hard.
Instead, you can use a /play command followed by the name of a properly set up text file, and your character will suddenly find himself playing Scarborough Fair. Or Rebel Yell. Or Blitzkrieg Bop. Or any of a plethora of songs you can make by converting a midi file over to the text using software available for download.
If that's too hard too, then go to a web site that offers the files for download and use those. It's what I did.
But this is a game... is playing music in the game really fun? Well, that depends on how twisted you are. If you're suddenly surrounded by hobbits, it's kind of fun to play All The Small Things. And Hotel California is always appropriately inappropriate in that setting. If you want to impress that hot Elven chickie, Jason Mraz' song I'm Yours just might get the message across. The only limit is your imagination.
And your music file library.
Better still; some people have set up multiple parts for multiple musical instruments. Some songs have a part for bass, drums, lute, horn, and so on. Several people with the appropriate file for each part get together in a group (or "fellowship." This is Lord of the Rings after all.) and they all start at once. If they're properly synched, they've got a band.
It's Guitar Heros of the Ring.