A quick solution would be to register an account on WordPress.com which offers free WordPress hosting. The only problem is that if you would like your own domain name it is not free anymore. Not that it is expensive, it is just not free. After investigating som other options i finally ended up using Google's Blogger. Maybe not bacause it is the best solution, but mainly because it covers my needs just fine.
As always it is very easy to get going, and the transfer of my existing posts from WordPress worked perfectly thanks to WordPress2Blogger. So after about an hour with configuring and converting this blog is now in the cloud.