The system requirements to run Magento are typically not found with most hosting companies. Here is a partial list of hosting companies that meet or exceed the system requirements to run Magento. I’ve also included a list of what it takes to run Magento so you can do your own comparisons.
I use Bluehost for many of my sites and they have been a very good provider and I am completely satisfied with their services. They currently have a “one click installation” script to get your Magento site running automatically. They have very affordable packages and lots of unlimited features that are standard. I highly recommend this hosting provider.
300 Gigabytes of Hosting Space - Host UNLIMITED Domains on 1 account for no extra cost - 5000 Pop/Imap Email Accounts - SSH Access (Secure Shell) - 3,000 Gigs of Transfer - SSL, FTP, Stats, CGI, Ruby (RoR), Perl, PHP, MYSQL, Front Page Extensions, Free Domain Forever, Free Site Builder, Free Search Engine Submission - Best Support in the Industry
Dreamhost is an employee owned hosting company that has very competitive hosting services. You can run your Magento installation here.
NEXCESS.NET specializes in hosting Magento-driven websites on its shared and dedicated web hosting plans, and has now become a .Platinum Partner. with Magento, as of April 15th. NEXCESS.NET currently hosts more than fifty Magento installations on their shared and dedicated hosting service.