Yes, I do. I don't have the money to buy 5 pairs of $100 cycling shorts, or to shower before I ride every ride, and I'd rather not wear something as underwear several different days without washing it. I don't have that kind of time or money, and it's simply way easier and cheaper to wash regular underwear.
I wear these:
http://www.rei.com/product/739770
Slick, synthetic, fairly breathable.