the problem with 1st cousins marrying is the greater chance of recessive genetic mutations or diseases coming through in their children. that risk is greatly decreased if you move out even one degree farther than that, say 2nd cousins.
That's the main reason you're not allowed to marry your first cousin. The laws first started appearing in the U.S. in the mid-1800s as victorian science dictated that such marriages caused idiocy.
And it's legal in japan, just not done very often.

yea its legal in some states in the U.S for 1st cousins to marry. also i think it might be legal in all states in the U.S. for 6th cousins to marry.