Drupal can run on virtually any hosting environment from the very inexpensive shared hosting plans all the way to dedicated servers, and everything in between.
However, some of Drupal's features require specific Apache, PHP, MySQL, SSH, GIT, Drush, Apache Solr, Varnish, APC, Memcache features that may or may not be available on any given hosting environment. Not all hosting companies support all the features that Drupal requires.
That is why we are going to periodically review and compile the list of all the best Drupal specific hosting companies here at www.drupalspecific.com.
Please let us know if you know any other Drupal-centric hosting vendor, so that we could include them in the above list.