The current fleet includes:
Galactica, Daedalus, Prometheus, Heart of Gold, Nimbus, Korolev, Red Dwarf, Serenity, Augira, Betta, Loenov, Sulaco, Moya, Odyssey, Star Bug, Swordfish II, Bebop, Cygnus, Palomino...um, those are all the ones that came to mind, but I know there are a few others.
S. S. Botany Bay?
That's a good one, seeing as it's the first time we see KHAAAAAANNN!
Oooooo...Botany Bay might win it on this round.
How about The Venture, from this [link] classic book which you all should read RIGHT NOW.
Okay, I have to tell my total geek Khan story. I did a show a few years ago in the Ricardo Montalban Theatre here in LA and at one point during tech while the crew was working on stage I ran up to the balcony, stood on the edge and yelled "KHANNNNNNNNN!" at the top of my lungs. Most people had no idea what I was doing but 3 of the crew almost fell over laughing.
Also, as a result of that gig I have Ricardo's voice giving the preshow announcement on my hard drive.
Yamato - sister ship to Enterprise in ST:TNG. It blew up due to a computer malfunction.
eta: Unrelatedly, the anime show
Space Battleship Yamato....
I think I have a Pegasus. It's the WinXP partition on one of my rental iMacs I think.
I do not have a Yamato. I'm going to add that to my list as well. It's also great because it is the ship from Star Blazers.
What was the name of the garbage ship in "Quark"?
The Black Bird - I'm on a BSG role over here.