One of the easiest ways to make an alien is to take an animal and make it humanoid, thus ending up with a sort of human-animal mixture. Fox-people, bear-people, walrus-people, and of course pig-people. To make slightly more exotic aliens, go beyond mammals: bird-people, snake-people, spider-people. This is about as far as most authors or GMs go, but you can push this further to get more alien aliens if you really try: termite-people, starfish-people, jellyfish-people, sponge-people.
Next time you're thinking of designing an alien for a game, think about pushing it a bit further out on the spectrum.
Transcript
GM: Two awkwardly waddling guards with unnatural looking tusked porcine faces intercept you.
Rogua: {a Gamorrean} Oink oink!
C-3PO: Goodness gracious me!
Ortugg: {a Gamorrean with an axe} Who sent you? Squeal!
[SFX]: < doosquee fidooby whiddle-boppity >
R2-D2: We're here for the auction.
Rogua: Which items are you bidding on? Oink?
C-3PO: Only the most expensive ones, of course!
Ortugg: Wallowing in cash, are you? Filthy rich?
Rogua: You don't look it. Oink oink.
Ortugg: Whaddya got? Silk purse? Full of pearls?
C-3PO: I'm made of gold!
Ortugg: I think they're telling porkies.
Rogua: Oink oink!