For the Federation, I think my favourite would have to the the Luna (Reconnaissance/Mirror Deep Space Science Vessel). With the right layout, she dish out damage better than the Defiants, last longer, and (IMO) look sexier doing it.

For the Klinks, I'd have to go with the Hegh'ta. She looks nasty, and she's got the teeth to back that look up. The universal BO layout is also a plus for me.

That being said, I so want the B'rel Retrofit. Too bad I can't afford it atm. Damn you economy!

Also, was anyone else disappointed with the Odyssey?

KDF - Vor'cha Attack Cruiser.

With the right build on it. It can take a pounding like a cruiser should. Yet can still dish out as much dps as some escorts. People get surprised by it, when I take it into Ker'rat.
I fly my Vor'cha with stock parts but swap the mission pod around. Depending on what type I fly.
Mirror - Tor'khat pod
Refit - Vor'cha pod
Fleet - Vor'Kang pod

FED - Akira Class Carrier.

Flying into battle with a wing of fighters is always fun. Watching them fly over the ship firing pulse cannons. Reminds me of those Ds9 battles. Plus the Akira just looks awesome.
I use the Thunder Child Saucer and Nacelles, with Stock Akira Struts and Pylons.

The one in my hangar

In game: Defiant (Can't remember what the class is actually called). It's just pure badass, except for the cloaking device which isn't worth much, except playing around with at Sirius.

Show/Movie wise: Intrepid Class. Coolest ship ever. The moving warp nacelles just make it even better.

KDF: None, as I really don't like any of the Klingon ship designs.

Lol, it really does look like a baby Vo'quv.

I don't really have favorite ships. Not yet.

Connie refit all day.