Birdgirl, I think I may know why breastfeeding reduces women's chances of getting breast cancer (i dunno about cancer in general though)... Most breast cancer tumors are estrogen dependant, and when breastfeeding, women's reproductive hormones are repressed- natures way of preventing another baby too soon. If estrogen is lowered, I would assume the chances of getting estrogen-dependant breast cancer would be lowered as well. Interesting stuff.

edit: I learned about the estrogen-dependant tumors in my Psychology of Sexuality class, but you can read more about it here Research Page: Control of Estrogen Production in Breast Cancer