Eh, what the hell...
Non-Star Wars? I've got to go with the NCC-1701-D... 7 years watching the TNG crew, and I'm simply hooked. Not to mention all the years of re-runs I've watched the Star Ship Enterprise continue its "Trek" through the galaxy... I love ST:TNG and wish it was on in the evenings more.
However, as much as I love ST:TNG, I gotta give props to an EU ship, the Moldy Crow...
Ship of Kyle Katarn and Jan Ors, the Moldy Crow is the ship that brings about Kyle's adventures in the Star Wars universe. He's Solo on Force steroids.
I dig Katarn, I dig his stor... I dig him so much I even dig his fan-fiction people did about his character making custom levels for the Jedi Knight game.
Katarn just rocks.
A close 2nd for me would be the Corellian Freighter "Otana". The ship owned by the Aazameen famaily during the "X-Wing: Alliance" games. The story's never been completed because the game was in development when TPM came out... It got cut short so TPM games could be put into production. That simply blows. A Star Wars flight sim completing the Azameen story is LONG overdue.
The Otana was a Corellian YT-series freighter... More advanced than the Millenium Falcon or Outrider... It's a kick-ass ship, and has a cameo at the battle of Endor. The storyline of "Alliance" is unparalleled to me... Lots of intribue, twists, and turns, and it fits perfectly. The Otana is a custom project of mine that I truly wish I had the time to focus on it.
So there ya go.