I agree with two of Eve’s areas, the only difference being that I keep trying to do these things anyway:
Math. I know that I’m bad with math, and my family and friends know that every electronic device I own has a calculator in it for a reason, yet I still regularly embarrass myself by trying to do math in front of others. Calculating discounts, how much the tax will be on a purchase, any tip other than 15% or 20%, how to split the check at a group lunch/dinner, etc. I think what happens is that I get it right just often enough to encourage myself. 
Sports. I’m almost completely useless at sports, but I love to play. I discovered softball a few years ago, and inflicted myself on two different teams. The first team was actually pretty good, but they kept me around because I’m a great team player: I have a good attitude, I’m reliable, I listen to advice and try my hardest every time, etc. And I never actually cost the team a win, so they were willing to let me stay. I never played sports as a kid – my family was very artsy, more into theatre and music and the like – but sometimes I wish I had. Even though I doubt it would help much. 
I nearly agreed with foreign languages, especially when I read, “I can speak just enough French to ask questions: but not enough to understand the answers!” But in my case I don’t think my problem is ineptitude so much as lack of practice. I last studied French about 1.5 years ago, and got through the university 202 level (with an “A” average). The next class would have been conversational French, but 202 was all I needed for my grad school requirement so I couldn’t afford (and didn’t have the time) to take any more French. I’d still love to practice my conversational French, because it’s the only language I have even a chance of becoming fluent in. Someday…
I agree with Kalhoun about the round brush/hair dryer, but will expand it to include hairstyling in general. I can’t do anything with my hair, and it’s not for a lack of trying! I just don’t get it. The same can be said for many cosmetics, too, though I’m slightly better with them than I am with my hair.
I agree with fishbicycle about gardening: I’m completely inept with any kind of flower or plant, indoors or out. The proverbial black thumb. And his username reminded me that I’m also somewhat inept at keeping fish alive … if I hadn’t managed to care for a cat for 18 years I’d be pretty concerned about my ability to keep anything alive. 
I can’t think of anything original to add, though I’m sure there are other things I’m hopeless at but just can’t remember right now. 