Listed below are some hosting services that have a good reputation and I recommend.
Lunarpages:
HostGator:
Bluehost:
Hostmonster:
Powweb:
From all the hosting services listed above, Powweb is the one without the usual CPanel and Fantastico that usually everyone is familiar with. So if you’re looking for CPanel or Fantastico, Powweb is not for you. But at the time of writing, Powweb is having a 50% off promo, so you might want to consider them or ask me about their service since I host my websites with Powweb.
Update: I am no longer recommend Powweb, as for my websites that I hosted there, I will only be using their hosting until the contract period is over. If you want to use Powweb as your hosting company, use it at your own risk.