Our system is really laid back, there's still some imperfections (I have relatively minimal experience with the original DND) but we've pretty much refined it only needing a couple of 1d20s, a 1d6 and some percentile dice. Sometimes we use Rolz (http://rolz.org) but other times I'll just roll for everybody (simplicity's sake).
I don't really like using classes, either, so I generally leave it open and let them sort of free-form their own rolls. Attributes (Strength, Intelligence, etc) ranges from -3 (terrible) to +3 (great) and can be changed around at the start and later on as they progress. Some story with gear, in long campaigns I make them work for it instead of just giving it to them.
And then for combat, I use percentage on ranged weapons (with modifiers). For melee confrontations, I roll for "initiative" and then I take the defensive bonus for the defender and the offensive bonus for the attacker and add them to their rolls. I roll two d20s (one is the attacker's roll, one is the defender's roll). If the defender has a defensive bonus of -3 (no armor, injured) and the attacker has an offensive bonus of +3 (quality weapon, skilled) then these numbers would be added to their rolls.
Sorry to leave a wall of text behind, but I figured somebody might find that interesting.
edit: oh yeah, the bogey system is pretty great too :lol:
59. Compulsive gambler, can’t refuse a bet
61. Spendthrift
63. Miserable
65. Depression
67. Paranoia
69. Distrustful
58. Born swimmer (x 1.5 rate)
60. Born climber (x 1.5 rate)
62. Sense of location
64. Empathy
66. Good luck (reroll any die once/session)
68. Gift of tongues, +2 starting languages
I’m Getting too Old for This Shit
Age goes up one category.
Reincarnated
You remember a life as someone else.
Photographic Memory
DM gives you hints on things you’ve seen before in better detail. Immune to Amnesia.
Bold and Beautiful
+1 Charisma, though you are prone to taking risks.