They can, but it was always a social tabboo years ago. The tabboo is based on sound reasoning - children of first cousins can inherit genetic defects which can lead to a handicapped offspring, although with modern technology and medical screening, this is obviously less of a problem than years ago.
depends where you live. here in NC, you have to be cousins 6 times removed by law. andy is right about the health risk of your own offspring. and you're gambling with your own life, should your child be born with problems. i would never do it. having healthy kids is worth more than money. if this is the situation you're in, move away, it's a big world out there, and there's a kazillion people you can meet.