Spelling Bee
I know people who would mock this, but when you really think about it, not a lot of people can spell. Seriously my high school science teacher was a bleeding vet. She knew everything, she was very scientific, and very intelligent. Guess how she spelled Turkeys. Turkies. Yup, people even misspell their own names!

I think anyone who can actually spell should get a gold medal.

Scavenger Hunts
It's not easy finding things. At least, it's not easy for everyone else. People lose keys, lovers, grades, or their own minds. Not only would it be a sport, but you'd learn how to find things or even better, not lose them in the first place!

Replacing the toilet paper
This would actually be very competitive for women. We all know how to do it, the question is who can do it faster, better, and more efficiently? It would be hilarious to watch the men do it. The first man to do it, no matter how poorly should get the gold. Because he now at least knows how to do it.