Dot-o-mator for iOS lets you check the availability of any .com, .net or .org domain name. Just enter the domain name in the check field, and Dot-o-mator will show you if its available or taken. If the domain is already registered, you can see when it expires, view the Whois info to see who owns it, or view the domain's website.
When you find a name you like, you can save it to your saved list, or email it to your email address. The email includes a link you can use to register the domains. (This app doesn't do the actual registrations.)
Version 1.1 also features a greatly expanded domain name generator. Just enter a word and select an endings list, and the generator shows you all possible combinations of the word with those endings. You can check the availability of all the generated names at the same time, customize the endings lists by adding or removing words, and create your own endings lists for even more name combinations.
Screenshots: (click to view)