A fun and easy twist on the game is to change up how you select the aliens for the game. The normal method is to deal out two and pick the one you like more. But there's plenty of other interesting methods for selecting your power. An idea called "Bid Drafting" was recently proposed and discussed on BoardGameGeek, which I recently tried out. It was a fun way to start the game and actually reminded me a little of Spice Harvest for Dune.
Some of the others I have enjoyed over the years include:
BOGGLE: This is a fun variation (especially in a set with over a lot of powers). Each player writes down the names of 5 powers that they would like to have, along with 5 powers that they don't want anyone to have. Read off the list. Any powers that are on more than one list are eliminated, and the powers that you wanted that are not on another list are yours. Each player may therefore have anywhere from 1 to 5 powers (If all of your choices are eliminated, you may pick one power at random). This allows for some creative thinking and allows powers that are otherwise fairly weak to be used to their utmost advantage.
DRAW STRAWS: Draw a number of powers equal to the number of players. Randomly choose a player to pick first. That player then takes all the powers and picks one for himself. He passes the powers to the next player clockwise, who repeats the process. The last player will get the least desired power. Then draw another set of powers and give them to the last player. He picks in the same manner as first player did, then passes counter clockwise. Powers should remain hidden until everyone has chosen both sets. This can be used for deciding between two powers, but more often it's used for double-power games.
PICK AND PASS: Each player draws three powers at random. One power they choose for themselves, the second one is thrown away, and the last one is passed to the player on their right. You may not look at the passed power until you have chosen your powers to pick and pass, etc. You must play the power passed to you.
TIDY BOWL: Deal 5 powers to each player. Put two powers "in" and the rest "out". All the "in" powers are shuffled together and dealt randomly.
More selection methods can be found on The Warp.