This is off topic for this section, perhaps you can move it one of the mods can, but it is technically possible. It isn't cheap though and isn't trivial. :-)
The other option is a Namecoin type of name which does not rely on ICANN or some centralized authority (which is often a good thing). This type of thing could be done with a namecoin-type clone, sidechains or other mechanisms. The drawback to these is that so far .bit (name coin) is not included in the top level name servers so you have to do some work to be able to go to <domain>.bit.
You are asking about GTLDs (Generic Top Level Domains). There is a lot of information out there if you are interested, here are a few places to start:
http://newgtlds.icann.org/en/http://afilias.info/global-registry-services/new-tldshttp://www.afilias.info/dotbrand
