Most people want to have a host that is reliable since that is one of the most important considerations. There are, of course, some people who don't consider reliability and are only interested in the host with the lowest prices. That might not always be a good idea.
People can probably talk best about their own personal experience. I've only had experience with 3 hosting companies: Verio, Interland (Web.com) and pairNetwork.
Verio was my first host. I started using them in 1995. I started using Interland in 1999. I used pairNetwork in the late 1990's and from 2002 to 2005. I last used Verio in 1999, so don't know how they are now from my own personal experience.
In my first post I mentioned that Interland (Web.com) and Pair Network are my two favorite. I also said that Web.com (Interland) no longer offers dedicated hosting. Web.com offers shared hosting and they have VPS (Virtual Private Server). PairNetwork has that and they also have dedicated hosting.
Even though I have used pairNetwork a couple of times and am not a customer at the present time. But they are still one of my two favorites based upon my personal experience with them. I have used Interland (Web.com) since 1999 and I am still with them.
Other people are going to have their own personal favorites based upon their experience with them and it is good to hear from different people. I hope some people will add their favorites to this thread.
When it comes to reliability, one of the best sources is information provided by Netcraft. They provide a daily report and a monthly report. There are some changes each month. Looking at their reports over a long period of time can be helpful in the determination of reliable hosting companies.
Here is a link to their report of the 10 Most Reliable Hosting Companies for the month of June, 2007 as well as the method they use to determine reliability
Netcraft: Tiscali is Most Reliable Hosting Company In June 2007