Yes, there are several options for hosting your site, and the one that works best for you depends on many factors. Here are some of those options:

1. Shared Hosting – what most of us have — ie GoDaddy. Affordable, limited support, slower page loads.
2. Dedicated Server – ie Rackspace. High cost, your own server, YOU are totally in charge of it.
3. Virtual/Cloud Hosting – lower cost than a dedicated server, fairly secure, hosting-only support, more complex then shared hosting.
4. Managed WordPress Hosting – ie WP Engine. More costly than shared hosting, easy to setup, easy to maintain, very secure for WP sites, fast page load AND WordPress Support!