Most hosting providers and personal installations on Unix/Linux systems should be able to host WordPress under very common configurations.
Please proceed to this page where you’d get updated requirements as WordPress continues to grow.
It is recommended you use a platform comprised of the Linux operating system, and either the Apache or NGINX webserver, but any server that supports PHP and MySQL will do. For permalinks your server needs to support mod_rewrite, or an alternative. Also your hosting is more secure when PHP applications, like WordPress, run using a separate user account instead of the servers default shared username. It is also essential that your host allows remote connections for many of the WordPress features to work. If your host blocks outgoing HTTP connections, many parts of WordPress might not function.
Hosting is a commodity these days and with a little digging, it’s easy to find a host that supports the above. If you’re looking for hosting suggestions, please try: