Justin Levitt, a professor at the Loyola University Law School and an expert in constitutional law and the law of democracy, with a particular focus on election administration and redistricting has done an exhaustive study.
Professor Levitt has studied elections since 2000, and while not exactly scientific its still very telling:
So far, I’ve found about 31 different incidents (some of which involve multiple ballots) since 2000, anywhere in the country. If you want to check my work, you can read a comprehensive list of the incidents below.
To put this in perspective, the 31 incidents below come in the context of general, primary, special, and municipal elections from 2000 through 2014. In general and primary elections alone, more than 1 billion ballots were cast in that period.
Some of these 31 incidents have been thoroughly investigated (including some prosecutions). But many have not. Based on how other claims have turned out, I’d bet that some of the 31 will end up debunked: a problem with matching people from one big computer list to another, or a data entry error, or confusion between two different people with the same name, or someone signing in on the wrong line of a pollbook.
The professor has found that the amount of voter fraud in the US since 2000 is approximately 0.000000031 %. He has also studied the other side of the - voter suppression:
In just four states that have held just a few elections under the harshest ID laws, more than 3,000 votes (in general elections alone) have reportedly been affirmatively rejected for lack of ID. (That doesn’t include voters without ID who didn’t show up, or recordkeeping mistakes by officials.) Some of those 3,000 may have been fraudulent ballots. But how many legitimate voters have already been turned away?
Considerably more Americans are being affected by voter suppression laws than are helping make sure elections are "legit".
No wonder our friends on the right are so eager to pass this legislation.