Fighter: the Thunder's crazy speed still makes it my go-to for point capture and interception assignments.
Frigate: really, my favorite is probably the Tempest (even cooler now with that drone), but since everybody's saying Tempest, I'll go with my new second-favorite, the Afflictor. It's the most fun of the phase ships to fly, in my opinion, and also the one that the AI handles best (I seem to lose a Shade every second battle I fight). The hardpoint ordnance is awesome—has anybody tried mounting four cluster bomb launchers and an AM blaster? Surprisingly effective (though it's only enough bombs, even with expanded magazines, to take down one cruiser, maybe two destroyers).
Destroyer: I'm finding the Sunder, since the recent patches, an absolute blast to play. Did it always have such strong flux capacity and dissipation? I remember it being really fragile, but outfitted properly now (lots of capacitors, hardened shields), it's like a little tiny Paragon. You barely even notice when a Sabot hits the shield. The autopulse laser finally being a decent weapon helps a lot too; I find the Sunder, in human hands, can beat pretty much anything up to an Aurora one-on-one (certain Eagle configurations are hard, though).
Cruiser: I actually always kind of liked the Falcon (it's a cool silhouette, it's cheap for a cruiser), but with maneuvering jets I really like it. Being able to get +35% range from an ITU on a ship that basically profiles as a destroyer (in terms of FP cost, armament, speed, and maneuverability) is just unfair. In the early campaign, I stick a couple heavy maulers on mine and go to town on all those big, fat, unshielded pirate Buffaloes from halfway across the map. Even setting the range advantage aside, the Falcon can outslug just about any destroyer and outrun any other cruiser.
Capital: Odyssey, hands down. Some things never change!