Not that unusual, or illegal. I know someone who has done it (actually 6 people - 3 couples made up of cousins in my family). All teen / early 20s and nothing lasting. None of the older generation found out and we all treated it as a huge joke.
However, many many regrets for everyone years later.
It isn't illegal, but it isn't particularly a good idea. The aristocracy were known as being blue blooded because there was so much inbreeding between cousins. Also, there was a this TV programme about the rise of genetic abnormalities in certain sections of the population, again because cousins were marrying each other.
I definitely wouldn't, and I would be really upset if a family member did, but we are a close family and it just seems really incestuous to me. Cousins are too closely linked genetically for me to think a sexual relationship is acceptable.
If there are inherited conditions in the family, then it would be prudent for cousins to have genetic counselling before having DC. Or if there had been previous consanguineous marriages in earlier generations.
WeAreEthernal has a point. From what I know children raised together don't feel each other sexually attractive. So, close cousins are not very likely to get together, particularly if they have been in close contact from and in early infancy. .
It certainly wouldn't go down well in my family (in fact I can't even conceive of it) but I do know a married couple who're cousins, who have kids, and no apparent abnormalities. I wouldn't frown on it for moral reasons.
In my younger days I might have had a hedonistic, sex, and drugs fuelled weekend with my mothers cousin's son. Was interesting arriving at a genteel family pub lunch afterwards - I genuinely don't know whether anyone to this day knew what we were up to but it felt very, very naughty. We didn't/don't really see much of each other though and certainly not a close knit family.