I thought Spacechem had the best high-score screen, giving histograms of three aspects of performance and showing where in each histogram your performance fell:
It's a quite clever solution to the high score board in the internet age; I've never really cared, even in score-based games, that there's some kid in the world who got 10,000,000 points, and it wouldn't motivate me to replay it if I only got 10,000. But seeing the whole histogram of scores, that's more motivating to me. (Like: there's a big spike in players that did something a bit better than you; you could catch up with them if you tried. Or: you're way ahead of the curve, maybe with a bit more practice you could be one of the best.)
The other nice thing is the thing you said, that it keeps track of several things. I like that -- a player might feel that a fewest-symbols solution is best, or a fewest-cycles solution is best, and the scoreboard doesn't try to impose one thing as best.
The fact that it's likely (or at least occasionally possible) that I'm better-than-average at *something*, or at least not terrible-at-everything, helps a lot with the demotivation aspect. I think most games have some opposed goals that make it hard to be better-at-everything but easier to be good-at-something ("most X gained", "fewest X lost", "quickest-to-goal", "longest survived", etc.) And if there aren't, well, there's an opportunity to add some more depth.