Doctor Crusher was my favourite character during my formative years. Cute, funny, smart, redhead, good dancer, and didn't take any trash.
Then, one day, I learned a few things. Firstly, Gates McFadden was the dance choreographer and fight choreographer for Labyrinth. Okay, cool. Ever see "Inside The Labyrinth"? There's a clip of her being horrendously patronising to a midget for being able to walk. Secondly, she doesn't like being reminded of her past. See this? This was taken a few years ago after I got her autograph. Now, everyone was lining up with shots of her as Doctor Crusher, but I went a little differently. I found out that she used to be a Muppeteer, and she had a little cameo on Muppets Take Manhattan, so, me being me, I got her to sign the DVD case.
Nowadays, Jadzia Dax, for pretty much the same reasons as Crusher. Apart from the lack of being a redhead.
Kirk. I totally believe one of the major reasons he enlisted in Starfleet was to bag chicks. ANY chicks.
All kidding aside, his era of trek was akin to the old west. Never knowing what was on the other side of the rise. He knew when to fight, and I know its had to believe knew when not to. He was fantically loyal to his crew and his ship to the point of scarificing his ship for a chance to save one of his best friends. And not only that he was will to give it his all, his everything, to protect people he had never met, like in Generations, his last thing he asked was "Did we do it? Did we make a diffrence?" He sacrificed his life to save billions of people, with only a handful of them ever knowing what he did.
Ok, so I have conditions, as much as I like Kirk I don't think he'd be such a great character just on his own. The people around him are very important to the.....well.....the Kirkness. He's the centerpiece of a great show, the main event and why you're there, but you need everything else around him to really make it great.
I love watching his quest for humanity. I respect Brent Spiner for his ability to portray someone as nearly human. Data's complete ignorance of many subtleties in human interaction lead to some of the funniest moments in Star Trek. Also, Data is a force to be reckoned with in a fight.
Tuvok is a definite personal favorite for me too. I like the little reminders that Vulcans aren't emotionless and they still have a personality buried under their facade; that reminder of course being Tuvoks sometimes brutal dry wit and sarcasm.
On the flip side of that coin I loved to hate Captain Solok, whose personality under the Vulcan facade was clearly of a pitiful egotistical bully.