In the United States state law governs marriage.

No, Ohio does not permit the marriage of first cousins.

Depending on local and state law, it is a marriage to a blood relative that is a cousin or closer. Some states allow marriage between first cousins, but the Federal Govt still frowns upon it...

The states of Alabama, Alaska, California, Colorado, Connecticut, DC, Florida, Georgia, Hawaii, Maryland, Massachusetts, New Jersey, New Mexico, New York, North Carolina, Rhode Island, South Carolina, Tennessee, Vermont, and Virginia all allow first cousins to marry.

First cousin marriages are also allowed in the following states under certain circumstances:

Arizona if both are 65 or older, or one is unable to reproduce; Illinois if both are 50 or older, or one is unable to reproduce; Indiana if both are at least 65; Maine if the couple obtains a physician's certificate of genetic counseling; Utah if both are 65 or older, or if both are 55 or older and one is unable to reproduce; Wisconsin if the woman is 55 or older or one is unable to reproduce.

First cousin marriage is legal in the UK and in many states in the United States. You can check which states at the link provided below. As for the rest of the world, there are many places where first cousin marriage is legal and you will need to research countries one-by-one.