You can move your WordPress site to any host that meets the minimum requirements to run WordPress. Hosts will be able to tell you if they meet the requirements, but if you need the technical details, you can find them here.
As for moving the existing site to a new host, check out the Moving WordPress article, which has a lot of information that you’ll need to know.
If you are looking to move from a self-hosted WordPress site to WordPress.com hosting, you should know that you will not have access to all the features available to you such as installing custom plugins and themes. You can see a quick comparison between self-hosted and WordPress.com here.
