I didn't realize there were enough shows that involve ships for this to be a category, but hey. My favorite ship on a TV show is definitely the U.S.S. Enterprise NCC-1701. The original ship from the original series. She's sleek, elegant, roomy, and iconic. I've spent more hours imagining myself aboard her than any other vessel. I even put together a model of her back in high school, which I still have. My paint job didn't turn out quite as nicely as this one, but you get the idea.
Oh, and if anyone wanted to buy me one of these as a gift, I would not complain! Who knew the Enterprise could be beautiful AND tasty?