A number of people ask me that question after reading my page about cousins, which explains first cousins twice removed and second cousins once removed.
Short answer: sure, unless your family has a history of genetic problems.
The Roman Catholic Church, which has had much more experience with people than the Unites States has, being bigger and older, frowns on it.
You must seek a dispensation from your Bishop to marry your first cousin. Where my ancestors came from, Monroe County Virginia (now West Virginia), before 1850 if people wanted to marry someone who wasn't an Indian, they had a choice of a cousin or nothing; it was sparsely populated.
Third cousins, then, have a great-great-grandparent as their most recent common ancestor.
"Removed" refers to how many generations "different" two people are.
It means that the closest ancestor that two people have in common is a grandparent.
(If they were any more closely related, they would be siblings.) "Second cousins" means that the closest common ancestor is a great-grandparent.
A cousin is a relative with whom a person shares one or more common ancestors.
When the cousins are not the same generation, they are described as "removed".
In this case, the smaller number of generations to the common ancestor is used to determine the degree, and the difference in generations determines the number of times removed.
(As the joke goes "Can a cousin, once removed, be returned? The short answer is "No, they're not the same thing." Let's take a look at what those cousin terms mean and how you can figure them out in your family tree.
Terms like "first cousin" and "second cousin" refer to what I call the degrees of "cousin-ness." It's an indication of how close the common ancestor is to them.