Actually it's not about doing it anonymously. I just want to GET some. But I can't because nobody knows me from Adam and nobody will trust me.
(Conversely, I won't trust anyone who now suddenly does ;-)
I tried to get verified via Bitmarket.eu but they gave up: I'm not active on eBay (only 1 transaction) and although I have a business Paypal account in good standing, Paypal and Bitcoin don't go together so well.
So what is the use of a digital currency you can't actually use online, to trade with people you don't know?
That being said: I still want some.
Edit: I've signed up with MtGox and that seems to work, save for the fact that I need to do a wire transfer to place funds there. Still, creditcards and European banking transfers are planned as options later this year. Thanks to both of you for comments and help!
Edit 2: Planet Money also had problems getting Bitcoin and had to do it face to face: http://www.npr.org/blogs/money/2011/07/13/137795648/the-tuesday-podcast-bitcoin