Here are About Web Search's picks for the Top Ten Domain Name Search Engines - there are a ton more than these ten out there, however, I've found these to be the ones that I've used most often and had the most success with. You can use these domain name search engines to check if a domain name you're considering is still available for purchase, or just to view domain name information.
1. Ajax Whois
Type in a domain name that you're thinking of and Ajax Whois will tell you immediately if it's available or not. You can edit what extensions you'd like to see on the right-hand side (.com, .net, .biz, etc.), as well as save your favorite domain name searches for easy access later.
BustAName not only provides a typical domain name search; they also offer tools to come up with a really good domain name. You can group idea word lists together, and BustAName will show you different possibilities - this is a great resource if you're stumped for a good domain name.
DomainTyper will finish the domain name as you type it, showing you if it's available or not. DomainTyper also has a nice domain name generator that you can use to brainstorm domain names.
Domai.nr is simple and streamlined: just type in a domain name that you're thinking about and Domia.nr will tell you quickly if it's available or taken. One interesting feature of Domai.nr - it shows you all the different possible domain names it might create.
Type in a domain name search at DomainsBot and you'll get an instant readout of availability, along with possible alternatives.
6. Domain Tools
You can do a simple domain name search at Domain Tools, but they also offer a useful assortment of domain tools: a domain name monitor, a brand alert, DNS tools, and more.
Domize is a simple domain name search tool; just type in the domain you're looking for and Domize will tell you in which extension (.com, .net, etc.) it might be available. You can save domain name ideas for later as well.
Dotomator is a fun domain name search tool. You can use the Dot-o-mator to create potential names, or use the Web 2.0 name generator for some random names from a word list you come up with.
Instant Domain Search does exactly what its name promises. No bells and whistles here, just a simple free domain search.