Not only that, but accidentally voting (e.g. because the person at the DMV said you could) can bar you from ever becoming a citizen and even get you deported:

http://www.immihelp.com/forum/showthread.php/91741-Denied-N-...

http://www.hg.org/article.asp?id=27445

http://www.gmanetwork.com/news/story/141110/pinoyabroad/pina...

https://beki70.wordpress.com/2011/03/03/fortunately-i-wasnt-...

Some states and local governments allow voting by non-citizen residents. They still can't vote in federal elections, though.