Yes it can be done.
Forget what you have read in the forums (Why can’t I redirect my blog? and Can I redirect my blog?) and don’t bother trying to get your head around the too technical product announcement (New Feature: Domains).
We have written a step by step guide on how to redirect your established WordPress.com blog to your own self-hosted blog on your own domain – Redirecting a WordPress.com Blog (PDF 739 KB).
Why do this?
We just like WordPress – that’s all.
Update: Based on the excellent comments, we have updated the original document to include a section on setting the permalink style to that used by WordPress.com – thank you everyone for helping us make this better.