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dreamhost.com - Is an almost full service web hosting provider. Their core competency is shared hosting but they do offer a dedicated hosting arrangement, but prevent you from having root access to your "dedicated" server.
They offer what they call a "private server" which offers some dedicated resources but is not quite a VPS.
I use Dreamhost for this site (and a couple others) plus because they offer tremendous data storage limits, my Dreamhost account serves as an offsite backup of my personal files.
Pair Networks was one of the earliest of the web hosting providers, and have remained independent for nearly 15 years. They provide an exhaustive array of web hosting plans, and they are a domain registrar (PAIRNIC).