I've played lots of songs but I "know" precisely zero too. I can't remember anything, even if I played it 10 minutes ago. I have to have the chord chart or sheet music in front of me. In one ear, out the other, getting old I guess.
Songs I would like to have stuck in my mental ROM...
1. Stuck in the Middle with You - Steelers Wheel
2. Love will tear us apart - Joy Division
3. Here Comes the Sun - The Beatles