I'm pretty sure the answer is "Yes", although there's certainly an urban legend around that to protect your identity you should put something like "See Photo ID" on the backs of them.
I recently received an email that said it was from a lawyer and had interesting advice regarding identity theft that included this trick.
It seems like pretty good advice, and I have tried it in the past. Trust me - don't experiment with this when you travel. The merchants hate it and I think the credit card companies do too. I think it's something legal.
I found Scambusters with this Google search: "PHOTO ID REQUIRED on credit card"
They say this specifically:
http://www.scambusters.org/Scambusters80.html
And they address a letter like it here:
http://www.scambusters.org/creditcardfraudprevention.html
They're right about hotel keys, which isn't in letter; however.
I did some more searching, and found this, too - a link from the Missouri attorney general's site
http://ago.mo.gov/ConsumerCorner/blog/10398/Should_I_sign_the_back_of_my_credit_card/
http://www.mytruston.com/blog/tips/sign_the_back_of_credit_cards_or_not.html
Truston is identity protection company, but they do link to the real visa rules, but does agree with what I found. Rules are 1 and 2.5 MB pdf files, I don't think I'll read them right now. :-)
Perry
AI and Voter Engagement
16 hours ago