TOS: Hard to pick one, but since I will it'll be Spock. Sacrilege to some I know, but he was just always overrated to me, more so than bad. Certainly not the worst in the franchise, and indicative of a strong cast him coming in last.
TNG: Wesley Crusher. Ugh. Gene Roddenberry's Mary Sue that can do no wrong, annoys people and can magically save the day no matter what. Ironically, my favorite Wesley episode was First Duty where he did screw up and didn't save the day. That was where he was the most "real" to me. Troi and Yar are close seconds.
DS9: This one's hard. I'll have to say Ezri. She was just redundant and was a distraction in season 7 from the otherwise epic arc of the whole season. Not only did she have a number of episodes dedicated to her, as if to compensate for her not being there the six years before, but half the B plots in the non-Ezri centered episodes revolved around her. Too much exposure, too much distraction. Ironically, my second would be Jadzia. She had three different personalities, the aloof smart person, the tongo playing drinker, and the Klingon valkyrie. None of them meshed together well. So yeah, guess it's Dax in this category.
VOY: Neelix. No contest. A jerk of the first order. He gets possessive of the kitchen to the point of being offended if people don't like his food, jealously stalks his girlfriend, just manufactures himself as being an expert on so many things, yet when put in those situations it's obvious he has no clue what he's doing, forces himself into every situation uninvited, and is a general dick in his "morale officer" duties, especially to Tuvok. He has no respect at all for other peoples values, and thinks everyone should accept his.
ENT: Archer.. what a bumbling moron, especially the first two seasons. No clue at all what he's doing, just fumbles around like a cowboy in space. His racism isn't becoming of his position at all, and I can't figure out how he got this command other than plain old fashion nepotism. Phlox comes a close second for being the most unethical doctor in the franchise.
NuTrek: Kirk... what a watered down version of an icon. Just a spoiled brat, bouncing all over the place, losing every fight he gets into, a walking hard-on with no sense of discipline. I've seen more mature twelve year olds. Then again the NuTrek Starfleet puts him in charge of their flagship and they wonder why their organization is apparently so corrupt a covert organization can just build a Super Dreadnaught in Earth's star system under the radar. They deserve what they get.
Overall.... Neelix. Why couldn't they have gotten rid of him when Seven came on?