Many online shops have the number 24 in them, to signify 24 hours a day – you may also be able to integrate numbers into your domain in a meaningful way to make them unique. Be careful though, because many cultures attach a lot of significance to certain numbers. Make sure that your number doesn't represent bad luck or other negative things in the country you're operating in.
Many registrars reserve the right to revoke your domain name for specific reasons, typically if you use the domain for illegal purposes or purposes deemed unacceptable (such as spamming). Many contracts contain a clause letting the registrar delete your domain name for no apparent reason. The implication, of course, is that the domain name is the registrar's, not yours.
Who is in charge of all of these processes? Most countries manage a Network Information Center (NIC). An NIC is the main database that has all the information regarding what domain names have been registered and the IP address associated with each of those domains. The nonprofit organization the Internet Corporation for Assigned Names and Numbers (ICANN) is in charge of creating and managing the procedures for internet namespaces.