I thought it was strange the first time I voted in NC when I didn't have to show any ID at the polling site. I believe I always took my voter registration card or driver's license when I lived in VA. Anyway, here I just had to tell them my name. The person at the desk looked through a book, crossed off my name, and handed me my ballot.
Personally, I don't think it is unreasonable to require some sort of ID, especially with all the fraud out there. Most people wouldn't have a problem producing a photo ID. For those who do not, perhaps a voter's registration card; social security card; or birth certificate would suffice. Honestly, what percentage of Americans don't have/couldn't obtain at least one of these reasonably?