Others are:
Lyran: Golden Pride Fleet (GPF)
Hydrans: Royal Hydran Armada (RHA)
Klingon: Klingon Dark Slayers (KDS)
Ministry of Kahless (MOK)
ISC: Not sure if they actually have a fleet name. But Karnak and Julin Eurthyr are both active Froggies.
(who said that?)
To Recap:
Fed: 1AF, SSCF, 9TH, FPF
Romulan: SOS, SPQR (although they'll deny it)
Klingon: KDS, MOK, KBF
Gorn: GDA
Kzin/Mirak: KAT/KOTH
Hydran: RHA
Lyran: GPF
ICS: ?
Other fleets that fly just about anything including other games:
Galactic Foreign Legion (GFL)
Xenocorp (XC)
But like the others said, fly a few of them first then decide. Get the full effect or enjoyment before you decide/commit.