Okay, the weirdest game I've ever seen has got to be Billy Hatcher by SEGA. You're dressed up as a chicken, and have to roll these eggs around (it's good to collect fruit by rolling over it), and once the egg's ready to hatch, you cock-a-doodle-doo at it, and it hatches.
Another close second would have to be Ape Escape. You're trying to sneak up and capture these monkeys, and they have sirens on their heads. They either run away or attack you, and you have different "weapons" at your disposal. I have this one, I think it's fun. The monkeys look like they're on crack, lol.
