Taxillus Transstellar
As of January 2013 Taxillus is no more. All capsuleers have moved to Alea Iacta Est Universal, an NPC corp, or other Corps not affiliated with AIE.
Corp Name: Taxillus Transstellar
Corp Ticker: TAXIL
TAXIL is a high security/low security corp for basically the rest of EVE. In highsec you can do low end missions (quests) or maybe some mining and exploration, all with the backup of an NPC entity known as CONCORD who will appear out of nowhere and blow up anyone who shoots you without just cause. Low Security space is a no-man's land where pirates roam free without fear of CONCORD. A great place for those who are looking for smaller scale PvP than is offered in 0.0 space. There are also missions and mining and exploration, and they are much more lucrative than anything you may be able to do in high sec but that reward is weighed against the risk of being blown up if you are not careful.