There is a playable lute in the game complete with animation (courtesy of Corepc and Sarkandar, respectively). The lute can be purchased occasionally from the various goods vendors and there is always one for sale at Jensine's in the Imperial City. You can also pick one up on the second floor of the craftybits warehouse, if you so desire.
The lute can be played to any NPC anywhere in the game. Player gets to individually pluck notes on the Lute and they will be analyzed for rhythm, tone, and flow. NPCs will either be offended at bad music or excited by good music. They will comment on your performance, clap, increase disposition and fame, and donate to your basket. If they get annoyed at your music they will vacate the premises.
Successful barding increases the disposition of your listeners, has a chance of increasing your fame and increments the speechcraft skill. Bad playing can decrease disposition and might even get you thrown out!
Playing the lute:
Equip the lute. It appears in the armor and clothing section of your inventory. When equipped a basket will appear on the ground in front of you. The lute is then played by pressing 1-6 on the keypad (Sorry, laptop users: you'll have to use the numlock key.) Each key press will play a short arpeggio.
The lute playing animation is now optional. Start the animation by hitting the right shift key. End it by hitting the return key. Its a little wonky, but *usually* works. Oblivion isn't designed to easily have players using custom animations. The biggest problem is that sometimes the animation won't quit. Use at your own risk, but save your game and give it a try.
Striking the first note on the lute will also silence the in-game music. It will resume playing naturally several seconds after you've played your last note. Its looks a little screwy from 1st person perspective unless you move your mouse around a little while playing. Looks great in 3rd person.
Un-equip the lute and the basket will vanish, making it much easier to pick up the goodies that your adoring public have given you.
Details for musicians:
Keys 1,2,3 are Ami, Dmi, and Emi (minor I, IV, V)
Keys 4,5,6 are Cma, Fma, Gma (relative major I, IV, V)
Just about any pop song should be sort of playable, though my experiments have shown that the people of Tamriel are not impressed with modern music.
For fun, try playing “House of the Rising Sun”
1, 4, 2 1, 4, 3 1, 4, 2 1, 3, 1