Yes, you can buy domain names without buying/having a HostGator hosting plan.
To do so, please visit http://hostgator.com/domains and purchase the domain you want. The domain registry tool requires credit card payment and is limited to .com, .net, .org, .info, .biz, .ws, .us, .bz, .cc, .nu, and .tv.
If the type of domain you want cannot be purchased online, or you need to pay with a method other than credit card, please email for assistance.