Dukat: Left alone after killing Sisko caused him to lose the last bit of sanity he still had. Without an enemy he doesn't have a scapegoat, and no one left to blame but the Bajorans, and eventually, himself.
Borg Queen: Some weird side effect of Borg Nanite infection...implied to be a nanoprobe virus-based STD, complete with spots around her mouth.
Tasha Yar: ANYTHING would have made her death better than it was. Hell, they could have had Data...overpower...her resulting from death from multiple injuries and THAT would have been more dignified than "just because." Personally, I would have had her killed like her counterpart who died in battle, but you get the idea.
CPT Kirk: Suicide via some space battle after finding out just how many incurable alien diseases he's contracted over the decades.
Barclay: Self-inflicted phaser wound. Not fatal right away -- he'd no doubt do it wrong. His would be a slow lingering death.
Female Changling: Like the Wicked Witch of the West -- she should have melted upon exposure to water. I would make it holy water (from a sacred Bajoran spring) just to be a *****.
Nero: It would have been cool if he was playing some Romulan stringed instrument while his ship was being destroyed. Spock had one, so chances are the Romulans had something similar.
Weyoun 8: Aside from the obvious bit of DAMAR killing him, I would have had Damar kill him slowly during an epic Cardassian interrogation. Think Chain of Command times 5. Then in the end Damar would put his pistol on its lowest setting and shoot non-critical areas until Weyoun dies.
Neelix: Vaporized by Tuvok. Quick, painless, humane. But above all, LOGICAL.
Captain Archer: Two words: Rura Penthe. Or possibly the Reman DIL mines. I know he didn't meet the Klingons and didn't have a chance to piss them off and whatnot. Okay, any excuse would do. Enterprise itself wasn't terrible, but I'm pretty sure Barclay would have made a better captain.
Dukat should have died alone in that cave after Sisko left, alternately weeping, laughing, and screaming at his voices.
His actions after that point can then be ported into an earlier, longer, and more personally responsible fall from grace for Kai Winn, making her arc in the final episodes less of an afterthought - distraught from the Prophets not speaking to her, she recreates an old ritual at the end of season 6 to force an answer from them, not fully knowing its association with the Pah Wraiths, and Jadzia inturrupts and is killed. Mortified, she destroys the artifact and hides the evidence, Jadzia never regains consciousness to reveal her killer. In Covenant, the leader of the cult is a new character, a Cardassian once known for mercy who had supposedly converted to the Bajoran religion but in fact had cultivated a Pah Wraith cult. Winn is with Kira upon discovering the cult, and is shocked and horrified, but still is seen removing an object from the station before leaving. Her actions in the final episodes proceed in the same manner without Anjohl's prompting, but her own growing desperation to find any divine answers at all.
One villain given a fitting death at the logical conclusion of his story, and another one given front billing in her own instead of being an unwitting sidekick to a washed up villain.