In no order...and if you can't think of 20, you're a pussy...
1. Pink Floyd
2. Radiohead
3. The Beatles
4. The Who
5. The Kinks
6. The Clash
7. The Ramones
8. Nirvana
9. Pearl Jam
10. Franz Ferdinand
11. Metallica
12. Iron Maiden
13. Powderfinger
14. Oasis
15. Blur
16. The Smiths
17. R.E.M.
18. Joy Division
19. The Buzzcocks
20. Pixies
Also I took "band" to mean just that. I mean, I love Bob Dylan, but he's not a band.