Most hosting providers and personal installations on Unix/Linux systems should be able to host WordPress under very common configurations.
WordPress server requirements for Version 3.2+:
PHP version 5.2.4 or greater
MySQL version 5.0.15 or greater
(Optional) (Required for Multisite) Apache mod_rewrite module (for clean URIs known as Permalinks)
» Requirements for Older Versions
It is recommended you use a robust platform comprised of the Linux operating system, and either the Apache web-server or the NGINX web- server. Almost any server that supports PHP and MySQL will work. If your host doesn’t support one of these platforms, and mod_rewrite, you will probably be better off switching to one of the many hosting providers that do offer those choices.
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 the WordPress will not function.
PHP 5.4 or greater is recommended.
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:
WordPress Recommended Hosts – these hosts support WordPress, in more ways than one.
Searching the WordPress support forums for recommendations