Hosts and registrar’s have different responsibilities. They both have supreme control your visibility online, and one should not use the same company for both – ever.
A host’s duties are to make sure your website is up, running, responsive, and give you support when something goes wrong.
A registrar’s duties are to keep your domain name safe, alert you when there are problems, and keep you in the loop on anything strange going on with your domain names. We’ve all heard stories about hosts who suddenly turn off a site and put the domain name on hold. If you host with the same company as is your registrar, you can lose both in a single moment.
If you keep your host and registrar separate, then if the website goes away, you can easily setup your site somewhere else (assuming you make regular backups) and change the DNS at your registrar. If you have many websites, use multiple hosts and keeping your website backed up at another host (behind a login so it can’t be spidered). If the site goes down at one host, change your DNS at your registrar and your site should be back up in a matter of hours (these days it takes a max of 24 hours for a DNS to re-propagate, and sometimes you can see it in a matter of a couple hours).
If your registrar freezes your domain, you’re in big trouble. Always keep another TLD or two of your site (and it’s good practice to own the .net, .com, etc of your websites) so that you can use another version why you work out the problems.
Use more than one registrar for those alternate TLDs. If you keep the .com name with your favorite registrar, the .net with a second registrar, and the .org with yet a third – you can usually recover while the resolution process is ongoing.
Own the alternate versions of your domain (at a different registrar) name pointing to your website. Make sure that those domain names 301 to your site and do not get indexed (you don’t want example.com and example.net both indexed with the same content as that will cause many SEO issues).
If your main domain is going to be down for a while (such as weeks or months during a lawsuit or a shady registrar); remove the 301 and let your site be re-indexed at the new domain. Unfortunately, you will lose most of your traffic as this will be considered a new domain and you can’t setup a 301 from a domain you don’t control (i.e. you can’t 301 your old domain to your new one as you no longer control that domain). When (or if) you regain control of your domain name, put the 301s back in place and return to your original DNS configuration.
If you have PPC or other media campaigns, change them to the new domain immediately. Don’t pay for traffic going to nowhere.
For information about 301 vs 302 see Matt’s post, you should be familiar with the difference depending on the circumstances of your site or domain being unavailable.
I’d also recommend trying to own the .com of your domain (which isn’t always possible).
My favorite registrar is Moniker.com. Register.com has one of the best APIs for bulk managing domain names and DNS entries. Both Google and Yahoo use MarkMonitor.com these days, which is good for large domains where you want to monitor a variety of domain uses (if this is your goal, also check out CSC Corporate Domains, INC which manages live.com). Google has a close relationship with enom.com, which has been a fairly reliable system. (Note: I have relationships with some of the above companies, but as with all my posts, this info is solely my opinions and I don’t receive funds from the above companies).
Worthwhile read (warning PDF file), http://www.cscprotectsbrands.com/pdf/029-031-TW-March_08-Searche.pdf, about domain tasting and searching for domain names.
Hosts can be cheap, and some cheap hosts are just fine depending on your goals and traffic. As with most things, you get a level of support based upon how much you’re paying. Pay for a cheap registrar, and you usually get zero support. When comparing hosts vs registrars, some people can get away with a cheap host. If you site goes down, it’s not that bid of a deal to move websites. Losing or having a domain name suspended can be devastating. Pay for a good registrar. Know your registrar’s policies. It’s easy to recover from a bad host, a bad registrar can ruin a business.