Although there have been several important diplomatic conferences on the neutral planet of Babel, when most members of the Federation speak of the Babel Conference they are referring to the one that took place in 2268. The main topic at this meeting of the founding members was the admission of Coridan into the United Federation of Planets. There were some objections to their joining, including the subject of illegal dilithium mining on the planet that both the Vulcans and Tellarites pointed out. However, Ambassador Sarek was able to gain a concensus to allow their admittance. (TOS: "Journey to Babel"), (TNG: "Sarek")
Also resolved at the conference were a number of security measures that were put in place to protect the space around Coridan.