You can pretty anywhere host WordPress on a server that meets the requirements (technical installation checklist). But with everything in real life some work better then others because there are differences.
From a developers perspective most things get solved on pretty any host anyway. That's good news for the average user because it means that you will get support for most of your problems. But it is nice to have important features met from the beginning so that things like auto-upgrade or installing plugins from the repository work flawlessly out of the box.
My compability check is that the hoster are properly configured in such a way, that the PHP-scripts owner is the same user executing the file in the HTTPD/FCGI environment. Next to this the PHP-scripts owner must be the user that is actually transfereing files to the server wether be it via FTP or preferable SFTP.
This check ensures that you will have the best update experience, which is important not only for WordPress updates but for updating and installing Plugins and Themes as well. Additionally if you need support, support personell will be able to better work and fix things on/for your blog.
This is not supported by all shared/dedicated hosters and often you do not have this information before you lock-in yourself in a hosting plan. Following is a list of hosters I personally was able to check while doing various tasks for WordPress users.
This list is not a recommandation for or against any of these hosts, it's a documentation wether or not they provide such a Feature.