I'm teaching myself a few songs on the accoustic:
Wake Me Up When September Ends
Boulevard of Broken Dreams
and a really nice song called Classical Gas.
As for piano, there are millions. XD I'll tell you the Green Day songs I taught myself:
Wake Me Up When September Ends (It pwns on the piano)
Boulevard of Broken Dreams
Are We the Waiting
Good Riddance (Time of Your Life)
Whatsername
Macy's Day Parade
I need to work on others, actually O.O
As for classical songs, there are so many...Fur Elise, Moonlight Sonata, The Tempest, Liebestraum, Cannon (by Pachabel), Prelude (By Bach), and a lot more...