It's best to get their company name and number and tell them that you will look it up and verify it before confirming any of your details.
Otherwise, that can be part of the process for ID theft. Obtaining your birthdate allows people who have some other minor details like your banking details, to obtain other things, and work their way onto something like Passports or their own bank accounts in your name. Or it could have just been someone trying to access your bank to transfer control of your accounts to them (I've been asked in the past for my date of birth as a form of ID when talking to banks and government agencies on the phone).
I generally refuse to give my date of birth over the phone, because if they can't prove who they are, why should I prove who I am at their request?
It could be as easy as making an imprint/photo of a Credit/Key Card (and signature) to get the card number and their name, and do a search in the phonebook for that name to get their address and phone number. Call up that number and get them to give their date of birth (for something bogus like a delivery confirmation, or as a bank wanting to verify a purchase or something serious to get you to want to help out), and then... well, let's just say that there are a number of things you can now do by phone or in person at certain banks with those sort of personal details. (this isn't a lesson for people to know how to do this - it is just to alert you to be aware of these sorts of scams that can have a real negative impact on you later - like all those courier/bank emails (I get) asking for you to confirm your details for an undelivered package (but is a virus in the attached 'details form'), or to log into a website (with some odd country code in the URL) to fix up something that went wrong on your account)
I use internet banking more than I should, but I still try to be careful and not interact with banks or anyone important unless I call them first, or see them in person.
I actually found this more disturbing - It was on TV yesterday, and there is probably a clip online somewhere, but this text article covers most of what was in the article.
Basically, it highlighted how you shouldn't leave any personal details on your own computer without at least password protecting those files, because repair shops could well be looking through your computer and stealing your details/files.
http://www.skynews.com.au/tech/article.aspx?id=354973
Sounds like you may have been a victim of card skimming. Your bank may have sent you an alert about this through email.
If you've ever handed your card to the waiter at a restaurant (or similar situation) they can put your card through a scanner to copy it's magnetic info AND your personal signature.
Alternatively if you've used your card at an ATM they may have scanned your card by installing a faux card reader and overhead camera (to read your pin when you key it in) on the ATM itself. The equipment they install are usually well sculpted and are not obvious unless you're deliberately inspecting.
To protect yourself, try not to withdraw cash from ATMs, especially ones that are isolated or facing the street where its not so busy (harder for them to install their gear if theres always people around), always cover your hand when you key in your pin and inspect the ATM for dodginess before use.
I suspect my local servo. I'm always extra careful at ATM's (the closest one to my house was on the news for the card reader/camera for you pin scam a couple of years ago) and I rarely use my card in person for anything else. I recently started using pin option with my credit card. My local servo has a security screen that gives the attendant a bit of privacy and they could easily swipe the card through a skimmer without you seeing, and then they have secuirty cameras to watch you enter your pin.
In business I see plenty of attempts at credit card scams. One of the most elaborate ones we get on a regular basis would only net the thief a couple of hundred bucks and takes a fair effort. It must be a constant battle for the banks to try and keep up with the thieves, and I'm impressed at how well they do.
Urge to buy toys... rising... rising! TERMINATED DUE TO LACK OF FUNDS
Al, As someone who deals with card skimming as part of my job, I can tell you that servo attendants are one of the "weak links" we come across in terms of people obtaining (and then usually selling) card numbers.
BTW the profits are there. They might only get $1000 at a time, but they'll sit there at an ATM with a handful of fake cards and just go nuts. Because the banks are often only able to respond retroactively because by the time they realise a scam is running the money is gone. Which is why it _is_ profitable ):
Eagerly waiting for Masterpiece Meister