- Assault Ship: Tough one! Jag would be up there, as would the Ishkur, Enyo, and the recently-upgraded rocket Hawk. I'm gonna go with Gallente/Enyo. It's hard to argue with that much DPS and tank, and it can take its DPS with it if it has to run away.
- Battle Cruiser: No question. Minmatar/Hurricane.
- Battleship: Another tough one. I'm gonna go with Minmatar/Tempest, though, for its versatility.
- Black Ops: Amarr/Redeemer, for the DPS.
- Carrier: Gallente/Thanatos. Though the Archon's abilities as a triage carrier are undeniable.
- Command Ship: Minmatar/Sleipnir. Claymore is also awesome, though the Amarr ones are also excellent.
- Covert Ops: Caldari/Buzzard, again for versatility.
- Cruiser: Not even a contest. Minmatar/Rupture.
- Destroyer: Same. Minmatar/Thrasher.
- Dreadnought: Right now, Gallente/Moros. After the dread drone nerf, though, Amarr/Revelation.
- EAF: Maybe a controversial choice, but I'm gonna go with Amarr/Sentinel. Death in a tiny package.
- Frigate: No question. Minmatar/Rifter.
- HAC: Another tough one. Probably Amarr/Zealot, though the Vag and Ishtar are also quite good.
- HIC: I personally like the Caldari/Onyx, though the Broadsword has a lot of fans.
- Interceptor: My personal favorite is Gallente/Taranis, though there are LOTS of good ones.
- Interdictor: Minmatar/Sabre, though all of them have their charms.
- Logistics: Minmatar/Scimitar, though all of them except the Oneiros are fine ships.
- Marauder: Amarr/Paladin. Does everything a Marauder needs to do, and nothing it doesn't. Though the Golem is also great.
- Recon: Toughest choice, for me. I love them all. But I think I'll have to go with Caldari/Falcon.
- Rookie Ship: Gallente/Velator, for the drone bay.
- Stealth Bomber: The Caldari/Manticore is so versatile, it's hard to pick anything else. But the Minmatar/Hound with its POS-bashing DPS is soooo tempting.
- Strat Cruiser: Caldari/Tengu, again for versatility, which is what strat cruisers are supposed to be about.
- Titan: For my money, the Gallente/Erebus, though the Avatar has a definite cachet.
And for the non-combatants with more than one race to choose from:
- Capital Industrial: Caldari/Orca.
- Freighter: Caldari/Charon.
- Industrial: Gallente/Iteron Mark V.
- Transports: Gallente/Viator.
Those are my choices. Where did I fail?
EDIT (24/Oct/2011): Certainly failed by forgetting freighters. Added my choice. Almost chose the Provi for how nice it looks and its (relatively) quick align time, but at the end of the day, what is a freighter about?