The Stillman Sisters from an episode of Charmed, entitled "The Power of Three Blondes". They are trying to steal the Halliwell sisters' powers and prove that they're more than just dumb blondes, and they come oh-so-close to succeeding at both.
Dr. Clayton Forrester of MST3K springs to mind. As his character brief in the show's official Episode Guide puts it, "His passion for depravity far exceeds his aptitude."
Harmony from Buffy the Vampire Slayer, after she became a vampire. She's evil, but other than that, she's still that teenage girl who wants to have friends and be loved. She is willing to kill her friends and allies, but at the very same time, she sincerely likes them and does not want them to be angry at her.
That said, the fact that she murders people to drink their blood (she is a vampire, after all) makes her somewhat less sympathetic.
This finally starts working for her in Angel, where she ends up being promoted out of the typing pool to Angel's secretary because she's a friendly face, admittedly one last seen trying to feed them to a group of vampires. Even when she betrays them again, Angel doesn't hold it against her, and actually prepared a reference for her so she can get a new job.
The Trio also start out this way. They quickly become less sympathetic — though not less ineffectual, however, as even Warren murdering Tara was an accident. He meant to kill Buffy.
Oh, no - Jonathan remains sympathetic, and actually becomes less evil as the other two get worse - he even helps Buffy defeat Warren. Andrew is less so than Jonathan since he enjoys committing crimes, but he's still so pathetic that even after he kills Jonathan (while manipulated by the First), he's such a failure at serving it that he's caught easily and held prisoner in Buffy's own house. Once he finally realises that real life is not a game, however, he shows enormous guilt over his actions, crying for the friend he killed and finishing his 'for posterity' recording by stating that not only does he expect to die, but feels he deserves to. He pulls a Heel-Face Turn and survives the final battle.
Peter Campbell of Mad Men. Sure, he's an obsequious little jerk who is looking for any opportunity to take advantage of any tiny opening. He's a total jerk to ANY and ALL women and he's so passive aggressive that it's sickening. And yet he's almost sympathetic because he's a constant failure with puppy dog eyes.
That was Season 1. Then Character Development kicks in. I'm not going to spoil the details, but by Season 4, he's possibly the single most sympathetic (in the sense that "you actually like him because he's a good guy") character on the show.
Peter becomes sympathetic when one realizes that he is trapped in the system just as much as the other main characters. His delusions are crushed at the end of season 1 and he realizes that being a jerk will not get him anywhere in the firm. He is much more humble after this and stops being a villain. Then he moves to Connecticut Suburbia in Season 5, and he starts cheating again...but is oddly still usually right (if dickish) about business.
Wiseguy. Mark Volchek runs the town of Lynchboro, Seattle as a personal fiefdom. The OCB is sent in to investigate him, only to find that his big plan is merely to build a cryogenic storage hospital for the entire town in order to sate his own personal phobia of death.
Crossing the border to Real Life here. Smoking Gun: World's Dumbest Criminals features quite a few of these. From the guy who broke in a convenience store through the roof, but couldn't get back out, to the group of guys who broke into a department store and stole all the display models (which have no working components).
Special mention goes to a pair of teens who walk into a police station and try to hold it up. This robbery attempt goes about as well as one would expect.
Col. Klink in Hogan's Heroes, to the extent that he and Col. Hogan clearly become close friends as the series progresses.
Governor Croque in Jack-of-All-Trades has a role similar to Klink's in Hogan's Heroes. He's not all that bad a guy, but more to the point, any likely replacement would either be more intelligent (and thus more likely to figure out what Jack and Emilia are up to), more tyrannical (and thus more likely to inflict suffering on the innocent people of Pulau Pulau), or both.
Crowley in Supernatural doesn't always fit this trope, but he's had his moments. He seems to flip-flop between wanting to be a badass demon overlord and sincerely trying to be a lesser evil, and his success either way is somewhat mixed.
After his first (unsuccessful) effort at double-crossing Lucifer in Season 5, the next time he meets the Winchesters he's on the lam, protesting to the boys "They killed my cat! They ATE MY TAILOR!" Of course at this point he's also on their bad side, as his bad information got Jo and Ellen killed.
After he succeeded in becoming King of Hell in Season 6, when summoned by Bobby to address the matter of the latter's soul, he popped a couple of Alka-Selzer in lieu of his usual glass of Scotch, complaining about the difficulties of trying to better the lot of his hopelessly corrupt demon brethren.
And of course in Season 7 he winds up living in hiding in a rundown house trailer after being ironically double-crossed by Castiel, who takes on the monster souls they had been jointly trying to acquire and briefly assumes the role of God.
Much like the Ferengi, the Centauri of Babylon 5 in general (and Londo in particular) seem at first to be too backstabby to be much of a threat. Of course, then, Londo gets in bed with Morden, and the Centauri start the Second Shadow War; but then, when Londo goes back to Centauri Prime, it proves that the Centauri have been sad little pawns the whole time.