dynamic initiative systems

Siege of the Citadel uses the chit draw system. That game is an unbalanced dice fest anyway, so it works fine.

Core Worlds has a random first player, with play then proceeding clockwise, determined at the beginning of the game and then the first player moves one place clockwise after each turn. I like that system, especially in something like a tableau-based deck-builder where turn order can screw you over a few times a game when it comes to buying.

Samurai Swords has a great system. You can bid some of your resources for turn order at the beginning of the round, but the interesting part is that you're bidding on the option to choose your turn order, not just going first. Another great thing about it is that if you didn't bid the highest your resources aren't wasted, instead you get your choice after the highest bidder. So if someone bids 2 koku for choosing swords and I bid 1, that person gets to choose first and I pick from what's left.