These are a few of the businesses and services that we use and think are awesome.
We use DreamHost to host all our sites. They're geeks like us, and are one of the few truly carbon neutral webhosts out there. Use our promo code ARCANEPALETTE to get $10 off a 1-year signup or $20 off a 2-year signup.
CoolHandle Web Hosting is a hosting provider that particularly cares about your WordPress site. They even have a marketplace right in their cPanel backend to find premier providers of WordPress themes and plugins.
page.ly is a hosted WordPress solution. Want all the benefits of a WordPress.com account with all the customizability of a WordPress.org self-install but without all the fuss of upgrading and being your own web administrator? page.ly is all about making your life easier so you don't need to worry about how your site works, just that it does work.
HostGator is a reliable and fast web server that we've used a number of times. They have excellent support and full root access (if you're into that sort of thing) on their VPS and dedicated serves.
Nexcess provides excellent web-hosting services with servers that are optimized for the type of site you are trying to run. I highly recommend the Magento- and WordPress-optimized servers.