Pretty much all I was going to say have been covered.
Others I would add.
My Name is Jonas - Weezer- Blue Album
Mexican Hairless - Toadies - Rubberneck
Homebrew - 311- Grassroots
None of these are songs these bands are known for but I've always loved these songs considering how much I used to listen to these CD's in high school.
This was the first song to enter my mind when I saw this thread existed. I also think Baba O'Reilly deserves it's place. Epic is always a good choice to open things up.
A few others I haven't seen mentioned:
The Rolling Stones "Brown Sugar" (Sticky Fingers)
Drive-By Truckers "Where the Devil Don't Stay" (The Dirty South)
The Hold Steady "Stuck Between Stations" (Boys and Girls in America)
Red Hot Chili Peppers "Power of Equality" (Blood Sugar Sex Magick)
Lee Bains III & The Glory Fires "The Company Man" (Dereconstructed)
Todd Snider "Age Like Wine" (East Nashville Skyline)
Willie Nelson "Shotgun Willie" (Shotgun Willie)
Trampled By Turtles "Wait So Long" (Palomino)