lulz at all the responses.
It's ultimately at the discretion of the merchant to accept the card or not. The merchant agreement states that a valid signature must be on the card, however after a couple years of use I've seen sig-strips absolutely unreadable in the past. It is perfectly acceptable, within merchant rules of course, to ask for some form of ID to validate the card and/or signature in the event that the signature on the card isn't usable. It is not acceptable to mandate alternate ID in order to complete a transaction using a card according to the merchant agreement. It is also completely acceptable for a merchant to deny service/sale for any reason except protected class discrimination, so there is obviously a contradiction of sorts as well.
Regarding SEE ID signatures - on all counts if the person's signature is not similar to that which is on the card, the card is not valid. It is accepted practice to check an ID as per above, but is technically against the merchant agreements for most processors.
To those that say a signature is hard to forge, it's not. Even low skill forgers get by quite easily, especially on many of the digital signature panels. Yes, as a kid I admit to having forged my mother's signature on my report card a couple times in order to hide a few bad grades. I believe this was in the 5th grade or so, and not even my parents questioned the signature when the next quarter came.
From personal experience, accurately signing the back of your card within that little strip is a pain in the ass in itself. Trying to adequately match signatures from multiple mediums is increasingly difficult.
Regarding SEE ID and signatures - it is far easier for someone to obtain a fake ID with a signature they themselves have written and thus are more likely to accurately match than a preexisting signature on the card itself.
Back in the day, I would accept cards per my manager's instruction that said SEE ID or similar, or weren't signed by using proper identification, but I would also inform the customer of the perils of using a card as such and the issues as detailed above of how much easier it is to use a stolen credit card as such, and also inform them that as per our merchant agreement I was technically not supposed to accept the card and the card was considered invalid.
Take it for what you will.