On the one hand, it seems only common sense that voters prove their identity by some government-certified document before casting their vote. Provided of course that such documents are not unduly hard or expensive to obtain (it would, needless to say, be a lot simpler if you just made those documents universal and compulsory as they are here, but I guess that's not to Americans' taste).
On the other hand, I've never seen any reports of voter fraud on any significant scale, so I'm not sure where that whole obsession on the Republican side comes from, either. It does seem like Republican voters are, on average, more motivated to vote, creating an obvious incentive for them to add a few hurdles to voting - but many of said hurdles sound eminently reasonable on the face of it, so seems hard to get too wound up about them.
