Two researchers at Old Dominion University have studied the issue and published their findings in the scholarly journal Electoral Studies. The Daily Caller reports they found:
We find that some non-citizens participate in U.S. elections, and that this participation has been large enough to change meaningful election outcomes including Electoral College votes, and Congressional elections. Non-citizen votes likely gave Senate Democrats the pivotal 60th vote needed to overcome filibusters in order to pass health care reform and other Obama administration priorities in the 111th Congress.To be fair, the article notes other scholars deny their finding. Still, it is worth investigating.
We've made registering and voting so ID-free essentially any scofflaw alien can vote, and all illegal aliens are scofflaws. I'll be surprised if we determine almost none voted.