Via MR, a fantastically in-depth Chessbase.com piece on how to think about reducing the number of draws in pro-level chess (there are a lot, for all kinds reason). As he notes, most proposals to reduce the number have been off-the-board rule changes, which is obvious, since changing the rules of the game aren't really feasible. It's chess after all.
There are variants to chess, which may have some efficacy in reducing draws, but usually they're too different from the beautiful game to be taken seriously. Anyway Gene Milener proposes Chess-3, a variant that remains true to the game, but with enough changes to reduce the level of draws:
Chess-like games can avoid high draw rates by having more piece power than chess has. The chess-3 answer to the challenge is to add power to a few pieces directly. This produces a nice corollary dividend in that the casual exchange rate is reduced, thus indirectly adding power by retaining it on the board. Yet another indirect anti-draw dividend is more imbalances, which Jeremy Silman emphasized are needed for decisive outcomes.