.org Domains - "The domain was originally "intended as the miscellaneous TLD for organizations that didn't fit anywhere else". It is commonly used by non-profit organizations, open-source projects, and communities, but is an open domain that can be used by anyone." - Wikipedia
Note that last part, "CAN BE USED BY ANYONE". Dot com domains are generally preferable over dot org domains, but shorter, memorable dot org domains can be had for much lower costs.
See below just a few of the 325 .ORG domains available at OwnTheName.com. Over 100 of these domains are 4-letter dot orgs. Check them out today.