Thanks, Legomancer. My reply was pretty harsh as well, but I was in shock, mostly because I like and respect you as a poster. 
I’m fond of dice, too, but I like to use 'em for Button Men or stuff like that.
Don’t mistake “diceless” for “rulesless”, or “rules light” for “no rules at all.” In Amber, for example (sorry to take a genre you don’t like, but I haven’t really don’t have much experience with other diceless games), has four stats, as Arden Ranger mentioned.
Psyche is taken by some GMs as your sensitivity to other people, your ability to manipulate them, and so on. So if your character has a high psyche, you as a player don’t have to be especially perceptive and pick up subtle hints that the GM throws in. Rather, the GM will probably feed you extra information (“He seems nervous . . . She appears to be holding something back.”) You also don’t have to have a golden tongue. Instead of rolling against your “Leadership” skill (or what have you). Instead, you can say, “I give a motivating speech.” Or, if you are a little more ambitious as a player, you can actually try to give the speech (“Ladies and gentlemen, we face a terrrible horrible awful enemy, and by golly by garsh, we gotta beat 'em! We just gotta!”) and the GM, taking your Psyche score into account, will judge that this was the Right Thing To Say to motivate the troops.
Taking a different example, I, personally, am no great whiz at strategy. Some people I’ve played with are military history buffs, and can describe at great length what their characters do with their troops. But, see, if I’m leading an army into battle against them, and their character has a Warfare of 10 and mine is 65, and our forces are roughly equal, then I can just tell the GM, “I do the right thing with my troops,” and, unless the other guy takes some sort of special action (bringing some new weapon onto the field, doing something clever with powers, or something like that) I’m going to be victorious.
I don’t have to look up my leadership skill, add in my terrain bonus, my troop bonus, my technology bonus, my magic bonus, yadda, yadda, yadda, and roll innumerable times to resolve the situation. I do have to respond to my opponent’s choices, or any weirdness the GM throws in, which, for me is more interesting than making die rolls and reading results off a chart. But I realize that for other people, the squidgieness of a diceless, rules-light system would be maddening. They want to have the numbers all laid out in front of them and they want the result settled by a dispassionate roll of the dice.
Certainly not everyone plays diceless in the way I describe. Possibly some of those jerks in the “We Are Superior Roleplayers” camp would consider it herasy. But I’m with you–I don’t want to be limited to characters who are only as suave as I am, only as smart as I am, only as strategic as I am, only as manipulative as I am, etc., any more that I would want to be restricted to characters who can only benchpress as much as I can. Part of the roleplaying experience, after all, is trying to realisitically portray a character who is different from you.