I <3 paradoxes. How about this one for starters?:
You go back in time and kill your dad before he gets together with your wife. Since him and your mom never got together, you can't possibly exist. Because you don't exist, you never went back in time. But if you never went back in time, then how did you kill your father? You aren't alive, so you didn't kill your father, so he's not dead so neither are you, so you go back in time and kill him and then you never killed him and then bring on the end of the frickin universe.
Another similar one:
You invent a time machine. You go back in time and destroy it right before you go back in time to destroy it. If you destroyed it, then you can't have destroyed it.
How about... here's one from a book I read.
You go back in time because the only cure for your mother's sickness vanished in the past and there's no way to reproduce it without going back in time. So you go back, and you get it, and then you go forward in time. But, on your way back, someone hitches a ride and jumps off a little early to make your mom sick. If you never went back in time, then your mother wouldn't have gotten sick and there would have been no need to go back in time. If you do, you make your mom sick and you have to go back in time to save her.
And...
You want to go from point A to point B. To do that, you must go half the distance. To get to the half point, you must go half of that half (a fourth of the way) To go that fourth, you have to travel and eighth, then sixteenth, and so on.
Jet fuel can't make dank memes.