In the case of voting, I think the need to prevent voter fraud outweighs the generic “You don't need an ID to exercise a right”i/i] argument.
When someone casts a vote, who is not eligible to vote, or when someone casts multiple votes, or otherwise acts to violate the integrity of the electoral process, the result is that everyone who had cast a legitimate vote has his voting rights violated, by having the influence of his vote illegitimately diluted.
I am all for requiring some form of verification, before one is allowed to cast a vote, that he is a citizen of the United States, a legal resident of the locality in which the election is taking place, and that he is not casting more than one vote. At the same time, I believe that this process needs to take place in a manner that imposes the least possible burden on the voter to meet these verification requirements, and impose the least possible intrusion upon the voter's privacy.