This is going to sound weird given my age, but... Sex. I am one of those rare people who is utterly bored by the idea of engaging in it. A lot of people even think there is something wrong with me or see me as some kind of threat over this (I'm not trying to prevent *you* from having sex - your life is your life, I just kind of think the idea of it for me is yawn-inspiring to downright weird). Maybe I'll have it someday. I don't know. If I get around to it. In the meantime, remember, folks, asexuals exist - you've just met one.
I guess I could say I refuse to sell my sense of personal honor and morality - like say "I refuse to hurt an innocent person," "I refuse to lie or to cover up something awful just to get 'ahead", but I'm not sure I should be so proud, because there's this niggling idea in the back of my mind that we all have our prices and we're all moral failures eventually.
I refuse to buy VitaminWater because their commercials really, REALLY annoy me. Watching television late at night while drifting off to sleep only to hear a commercial SCREAMING at me about gorillas makes me go "No, not buying your product - EVER."