Someone I play with got really frustrated at getting perpetually bad rolls in Settlers of Catan, to the point of no longer wanting to play. So I wrote down two copies of all possible rolls (such that they end up weighted appropriately) on small pieces of paper, and we cycle through them all. For that game, at least, it feels much better and feels more "fair". (It does add an element of "card" counting, but none of us are serious enough to pay that much attention. At most, we remember whether the 2 or 12 has come up yet.)
There's an interesting "mod" for games involving die rolls where you replace each dice with a set of numbers that the player can just pick, with the limitation that each "die" must use each number once before reusing any.
