A little while back I was reading about the sphere builders seen on Enterprise and got to thinking, could there be a United Federation of Planets without Earth? I'm thinking the sphere builders would've been better off having the Xindi take out other key members of the Federation as well as Earth!
Well, the impression that ENT seemed to give is that it was Humans who were able to act as the "honest brokers" who brought Andor, Tellar, and Vulcan together in a federal union. Apparently without the influence of Humans -- and presumably their victory over Romulus in the Earth-Romulan War -- the Federation would never have come into being.
The novel
A Less Perfect Union by William Leisner from the
Star Trek: Myriad Universes anthology of alternate
Star Trek universes featured a timeline in which Terra Prime became a major political party in United Earth in the 2150s. Because of Terra Prime's isolationist influence in the United Earth Parliament, U.E. withdrew from the negotiations to found the Coalition of Planets, which collapsed. Captain Archer and the NX-01 crew continued their campaign to create a coalition without Earth, however, and Vulcan, Andor, Tellar, and Denobula eventually founded the Interstellar Coalition at Babel in 2161, which was a sort of European Union-esque coalition of worlds less strongly integrated than the Federation in the Prime Universe. Unlike the E.U., though, the Interstellar Coalition maintained its own military, the Interstellar Coalition Space Command, whose vessels received names like the
I.C.V. Shallash. (United Earth Starfleet vessels ended up receiving the prefix "U.E.S.S.," for "United Earth Starship.")
The Interstellar Coalition and United Earth became major rivals for over a century before the government of United Earth Prime Minister Carter Winston eventually applied for Coalition membership in the 2260s.
ETA:
Another
Myriad Universes novel,
The Chimes At Midnight by Geoffrey Trowbridge features a timeline in which the death of Spock in childhood prevents him from determining that the Whale Probe sought out humpback whales, preventing Kirk and Co. from traveling back in time to stop the Probe. Earth is devastated by the Probe, and the Klingon Empire takes advantage of the chaos to conquer Earth. The Federation government evacuates from Earth during the battle and re-locates. Vulcan becomes the new Federation capital planet, and the Vulcan High Command building in ShiKahr seen in ENT's Vulcan Reformation arc becomes the new Federation capitol building (replacing the Palais de la Concorde in Paris).