I have used Warped.com for years. In that time I may have had one instance of my site being down. I like them, because their tech support is very responsive. My domain is hosted with them, and I currently have two Wordpress sites installed in my domain.

I've been hosting my WP sites on pair.com for many many years. I have two Wordpress sites running there, yipezine.com (which is an independent install I did) and westercon66.org, which is using an install I did via the maintenance tools pair offers.
We found PAIR because it was the provider for the Sluggy Freelance webcomic (don't know if that is still true)

I've been using Inmotion for almost a year now, and it's been pretty reliable. One incidence of being down that I know about. That said, I'm pretty low-level.

I use http://dreamhost.com/ (who offers wordpress support, though I don't use that feature).

They seem reasonably reliable up-time-wise.

That said, there was a recent problem about some sites getting hacked where it came out that some of their password policies were very dubious (apparently they don't strongly hash your account passwords, but rather encrypt them so they can be decrypted for "password recovery" - stupid!) and they were supposedly going to improve them.

Edited to add: I hit the wrong reply button; this wasn't meant as a specific reply to joycemocha. :)

Edited at 2012-10-09 02:07 pm (UTC)

I recently switched my hosting to dreamhost as well. This allowed me to consolidate my nameserver/DNS (from the loathsome Go Daddy) and hosting services (from... damn, someone so awful I can't even remember anymore). Have been very happy with them... they do a fine job serving up my 6 pageviews per month.

While I use dreamhost (since forever) for all my sites, we switched my previous day job's site to inmotionhosting becuase not only do they have stellar reviews, they have *really good* customer service that does not assume technical knowledge. (Dreamhost works best, imho, if you have a fair stock of webmastering beneath your belt.)

(we switched from hostgator, which I *do not* recommend; her site (family portrait photographer) got hacked with porn, including child porn, multiple times, and they pretty much refused to help us with it other than to threaten to close the account if we didn't get rid of said porn.)

Laughing Squid is a web host from the Bay Area. It's been around for years, run by many of the Well founders and it's been reliable. Not very expensive either.
Anon

I have all my sites on a boutique server run by a pal back in the midwest. Very private, high level of service (there are only few dozen clients or so). Does not have 24/7 support, but you get to deal directly with the owner as well as the technician nd primary client ;)

He also does email with hand-tuned spam filtering.