Joker from The LEGO Batman Movie, like many of his other incarnations, commits many of his crimes (like blowing up Gotham and sending the debris into the Abyss of Nothingness) just to get Batman's attention and impress him. Here though, none of Joker's plans have ever worked to the point of Gotham's citizens not really taking him seriously any more. Batman even tells him that he has no investment in their antagonistic relationship, claiming that he has more emotional investment against Bane and Superman than he does Joker.
"Bowler Hat Guy" in Meet the Robinsons. He becomes dramatically more sympathetic as the movie progresses, and by the end of it he isn't even the villain.
Megamind. You start to root for him since, despite his numerous failures against Boring Invincible Hero Metro Man, he never gives up. He always bounces back from his latest plot being foiled, ready to go at it again.
Captain Hook. Unlike other Disney villains, he has an understandable reason to want to destroy his nemesis (who seems to continually make his life miserable for no reason). He's constantly humiliated throughout the movie, seems disrespected by everyone in Never Land (besides Mr. Smee), and isn't feared in the slightest despite being clearly murderous. And there's the fact that the narrative oddly takes sadistic liking making him the butt of the many comical injuries.
The captain's ineffectiveness continues in the sequel, Return to Never Land. They tried to make him more cunning and unappealing (his crew, this time, seems to respect him, even), but yet, somehow winds up as more of a bumbling, unsuccessful fool than the original. His own ship even gets destroyed.
How about Mr. Smee, a rotund nincompoop First-Mate of Hook with a jovial voice, but eager to abet the most heinous deeds on the excuse of Just Following Orders.
Really though, you could count Captain Hook and his crew as a whole. They're not exactly angels, yes, but they do have their reasons, and constantly get the short end of the stick, only getting close to victory somewhat and having it brutally taken away. Seems as though Failure Is the Only Option.
Films — Live-Action
Prince Edward in Braveheart. He tries so hard to meet his father Longshanks' expectations, but he never does.
The Newspaper Boy in "Better Off Dead."
Jerry Londegaard in Fargo. You can't help but feel something for him when you understand his situation, although, considering ended up getting his wife murdered, he's not entirely sympathetic.
RoboGadget, the evil android duplicate of the protagonist of the film version of Inspector Gadget. He actually makes the iconic Idiot Hero look competent when they confront each other.
Justin Hammer from Iron Man 2, though more "ineffectual" (and humorous) than "sympathetic". More to the point he pretends to be an Evil Counterpart of Tony Stark, but is actually a pompous clown whose products are of very poor quality, whose attempts to intimidate the actual villain of the movie would work better on a five-year old, and whose henchmen are incompetent rentacops who carry mace and tasers.
"He's no good, but he's what I want. I'm not a nice person, Laura, and neither is he. He knows I know he's just what he is. He also knows that I don't care. We belong together because we're both weak and can't seem to help it. That's why I know he's capable of murder.note Keep in mind that she says he's capable of murder. He doesn't actually do it. He's like me."
Peter Lorre — as he was frequently typecast the "Sad Monster" after M — got to play quite a few of these in his career. Casablanca, The Maltese Falcon, Arsenic and Old Lace, and in pretty much all of his later career, particularly in his team-ups with Vincent Price.
On the other hand, Elisha Cook, Jr. made Peter Lorre look lucky. At least Lorre survived most of the above examples (and in Arsenic and Old Lace, he even pulled off a Karma Houdini). The same can't be said for poor Elisha in Phantom Lady, The Big Sleep, Born To Kill (where, shortly before his character's death, he tries to menace a little old lady, only to have the little old lady kick his ass!), or The Killing. In Shane, he's practically a good guy version of this trope. But the best example of how much worse off Cook is compared to Lorre is in The Maltese Falcon, where they're both ISVs. Sam Spade disarms and humiliates Cook's Wilmer far more often than he does Lorre's Joel Cairo, despite the fact that Wilmer's a multiple murderer and Cairo isn't. And at the end, their mutual boss (and possibly more) Casper Guttman sells out Wilmer to the authorities while happily walking off arm in arm with Cairo (although they all end up in jail). Joel Cairo may be more pathetic than you, but Wilmer is even more pathetic than Cairo.
In I Wake Up Screaming, where he's both the murderer and a pathetic weakling, he just goes to jail.
One critic said of Cook that 'his very appearance seems like an invitation to destroy him'.
Things have turned around for him by the time he plays the mobster Icepick in Magnum, P.I. who inverts it.
Inspector Clouseau, inverted this, as he originally was intended as an incompetent version of Inspector Javert in the original The Pink Panther (1963), but he managed to be so much more sympathetic than protagonist Charles "The Phantom" Lytton that he was retooled into the protagonist of the film's sequels who was still a moron but with lady luck on his side.
And THEN, in Son of the Pink Panther, Dreyfus gets a reboot into sympathetic, if not protagonist, at least The Woobie status, as his complete descent into Axe-Crazy has apparently been retconned out of existence and him back INTO existence. He even gets the girl with the down side of now being the stepfather to his late nemesis Clouseau's long-lost son. Still the Butt-Monkey, if not the ISV.
Repo! The Genetic Opera has Amber Sweet. She's just as nasty as her brothers, but she's usually too high on zydrate to be effectual.
And Luigi and Pavi aren't much better, given that Luigi, despite his claims that only he's got brains enough, comes across as a simple minded Knife Nut and Pavi spends most of his time staring at his own face in the mirror he forever carries with him. That being said, Luigi is quite effective in the "stabbing people for no good reason" compartment, which makes him the least harmless of the Largo siblings.
Gargamel, mostly, comes off as this in The Smurfs. Until he gets his hands on Smurf Essence, that is.
Muerte ("name for death!") in Undercover Blues. Muerte's reputation on the streets is hinted at as being formidable, but his utterly humiliating defeat at the hands of Jeff Blue quickly turned him into one of these. Every lost tooth just makes him that much more lovable.
The Elite Squad: Fábio Barbosa is a Dirty Cop yet unlike other antagonists in the series who are violent and realistic depictions of Brazilian drug lords and corrupt policemen, he comes across as a pathetic, spineless Butt-Monkey who gets beaten and berated in the first movie, and in the second one, he is bossed around by his own subordinateMajor Rocha. With that said Fábio is the one to actually kill Rocha himself rather than the protagonists and its implied he becomes a Not-So-Harmless Villain in the epilogue.