Anyone can walk into a polling place and vote in your place. All that your impostor needs do is be able to roughly forge your name on the ballot application. This, of course, facilitates all kinds of fraud.
Now, however, an increasing number of states are considering new laws that would require a valid voters ID. This, of course, flows from fears that increasing numbers of non-citizens--especially illegal immigrants--are voting and, in effect, stealing your franchise. Any measures requiring ID proof will be opposed by immigrant "rights" groups that believe mere presence in the United States qualifies for all rights of privileges of citizenship.
For a balanced analysis of the issue, read this article from the National Council of State Legislatures.