If it's wordpress to wordpress then it's just a matter of exporting all the posts in XML format (I think it's in the manage menu) and then importing them in to the new wordpress. You even have the ability to select a box which automatically downloads the images of the old blog to the new blog.

The only problem you might see is if you migrate to the same domain name... the images might not copy in this case. If this happens then export to another name (maybe backup.mydomain.com) and then export again from that to mydomain.com.

The whole process is fairly painless.