1) HERO 5th
2) 3.5 D&D
3) Traveller
4) Deadlands
5) Paranoia
Note: Lots of games got left off, of course. The ones I listed either have a system I particularly enjoy, or just simulate their settings better than anyone else on some level.
I'd love to have my 2nd favorite game, M&M, but
HERO (my fave) covers the same ground...well, really, it covers everything in some sense.
CoC and
Shadowrun are absent as well, despite my love for them. I'd love to have games like
MechWarrior, Godlike, Space: 1889, Mayfair's
Underground, the WoD games, the extremely creative
RIFTS setting or any of the Chaosium "Eternal Champion" RPGs, but mainly as sourcebooks.
EDIT: but the real question is, what would I use instead of dice?
Well, Gilligan, what about woven reed bags filled with number chits carved from coconut husks?