In 26 out of 50 states in the United States, and most other countries, first cousins can marry. Second cousins, third cousins, first cousins once removed, and any other cousins except first cousins can marry in all 50 states and every country in the world. The Roman Catholic Church, which has had much more experience with people than the Unites States (It has more people and has been around longer) lets first cousins marry. So, most of the world has no objections.
The above is according to, http://www.tedpack.org/cuzdate.html