In Baccano!, this spot is owned by Dallas Genoard, who isn't all that sympathetic, but is more than ineffectual enough to make up for it.
Bleach: Lilynette, Stark's Token Mini-Moe fraccion. She's currently fighting Ukitake, who is one of the 5 most powerful shinigami in existence. The fight so far has consisted of Ukitake telling her that he doesn't want to fight a little girl and simply deflecting or dodging every attack she threw at him. Currently, he's playing keep-away with her Zanpaktou as she cries at him to give it back and threatens over and over again to kill him. Ukitake even lectures the girl on how her determination is admirable, but she simply lacks the ability to 'fight' him properly (i.e take the sword back). She fires a cero, he deflects it with his hand. No wonder she was pissed off.
Jeremiah Gottwald from Code Geass, who began the show as the military equivalent of a Jerk Jock, but made the mistake of crossing Lelouch, which left him disgraced, hated, and saddled with the ignoble nickname "Orange". His enormous popularity spared him from a planned quick death, resulting in his returning later as an Ax-Crazy cyborg. Just to crank up the sympathy another few notches, the side materials revealed that Jeremiah was a palace guard on the day Empress Marianne was killed, and based his entire career on an attempt to atone for failing not only Marianne, but her children, who disappeared in Japan, leading him to think that they were killed by the Japanese, which prompted his racism against Elevens, which resulted in Lelouch (Marianne's supposedly-dead son) publicly humiliating him. Whoops...In the second season, Jeremiah was sent by the Geass Order to assassinate Lelouch, revealed that he was still loyal to Marianne, and when Lelouch admitted that avenging his mother was one of his main reasons for becoming Zero, "Orange-Boy" immediately dropped his thirst for vengeance and became Lelouch's retainer.
Buaku from Dominion Tank Police and his sidekicks, the Puma sisters. They've always been wannabe Magnificent Bastards, but they were slightly more competent in the manga. Granted, their failures are rarely their own fault, discounting their lack of foresight.
Emperor Pilaf and his assistants from Dragon Ball. Only once does Pilaf (almost) get what he wants...he manages to successfully get a wish from Shen Long in the first episode of Dragonball GT. However, instead of wishing for what he wanted, he shouts in frustration at Goku (who showed up just as the dragon was summoned) "I wish you were a kid again!" - not as an actual intended wish, but because Goku was so much easier to defeat as a child.
Except that he has come close to getting his wish twice (or once, depending on your opinion of DBGT in general. The other time was back when he first appeared in Dragonball. He managed to summon Shenron but took so long to make his wish to  that Oolong, the transforming pig, managed to fly over to the dragon and wish for girls panties, which he then proceeded to wear on his head for a while.
Excel in Excel Saga at times. She really wants to help her Lord Il Palazzo's plans to take over the world, but she fails so badly at every mission given to her. Often subverted though by following a sympathetic moment with doing or saying something disturbing.
Fighting Foodons: You really can't help but feel sorry for Claw dia after all the times that she fails throughout the series, especially when King Gorge attempts to kill her for failing him for the last time. Luckily, Chase and the gang were there to stop him and chase him off (as he would've completely killed her off if it weren't for them returning her to her old self and redeeming her through Chase's tasty cooking).
Principal Uchimiyada on Great Teacher Onizuka often plots to get rid of Onizuka, and yet is portrayed as less of a threat than the troubled students in Onizuka's class, like Miyabi, Urumi, and (towards the end of the manga) Sho.
Zeta Gundam had Jerid Mesa, who ended up becoming the Designated Rival for the show's protagonist, got into a vicious cycle of each killing the other's friends and/or lovers in battle, and eventually was killed when the hero threw his mobile suit into an exploding battleship.
Mobile Suit Gundam 00 had Patrick Coulasour, an ace in 'simulated' combat, who quickly develops a one-sided rivalry with the Gundams after being publicly humiliated by them in the first episode, only to be dispatched in a similar fashion when he returns later. As with Jeremiah, fans latched onto him, giving him the nickname "Team Patrick". He eventually latches onto his commanding officer, Kati Mannequin, and goes on to be shot down another 5 or 6 times, even after switching sides. Unlike most, he actually does become a competent pilot by the end of the show, though nowhere near Ace Pilot status.
Carta Issue of Mobile Suit Gundam: Iron-Blooded Orphans zig-zags between this and Not-So-Harmless Villain. She is a valorous Large Ham Gjallarhorn officer who overly relies on team formation and frequently talk mid-fight. The ineffectual part comes from her belief in honor when her opponents obviously have none and have no qualms about killing her off guard. While her knowledge of formation is actually put to use when she went after Orga's mobile worker to disrupt his command, only to be halted by Biscuit's Heroic Sacrifice and her combat skill is decent for a person who enters the field for the first time with a ceremonial weapon, her urge for Combat by Champion frequently backfires. The sympathetic part comes from her tragic death, both delivered by Mikazuki and staged by none other than her treachous love interest, McGillis. In the end, Carta is just an honourable soldier who wants to honor her family, not only it doesn't earn any respect, it nets a Disproportionate Retribution from her enemy because of her unintentional killing.
Heavy Metal L-Gaim's Gavlet Gabre is a particularly jarring example. He's introduced as the primary rival, but never once defeats the protagonist, Daba Myroad. During the final battle at Sveto, he fails to defeat the unimportant and generic villain Rockley Ron, which makes the later the sole villain who makes it out of the show without being captured or killed.
Kurumi, Kurumi, from Kimi ni Todoke. As of the end of the anime's first season, she still hasn't caught a break despite confessing to Kazehaya and tearing down what was left of her fake persona — or if she has, it was offscreen.
Kinkotsuman and Iwao from Kinnikuman are complete losers, plain and simple, who can't seem to do anything right. Of course, they're also kind of a subversion, because Kinnikuman is just as big a loser. Also, sometimes, when they aim high, they miss high. Like when Kinkotsuman accidentally shot Terryman in the leg when he was aiming for Kinnikuman, and Terryman ended up having to have his leg amputated (this is only in the manga, since in the TV series, Terryman eventually gets better, but the toned-down anime scene still is sad for poor Terryman).
In fact, in Nisei, Kinkotsuman's son, Bone Cold's, entire motivation as a villain is distancing himself from how lame his dad was.
King Dedede in Kirby of the Stars is the kind of guy who wants respect from the Cappies, and just wants to beat up Kirby for the sake of it, which is why he buys Demon Beasts/monsters online from Holy Nightmare/Nightmare Enterprises. Of course, Kirby always wins the day, so Dedede never gets the respect he wants. To be fair, Dedede isn't really all that bad, he's just mean, misunderstood, and a completely incompetent half-wit.
The Laughably EvilGonk, Foxy the Silver Fox, particularly in the anime where he gets more screen time. He's relatively Weak, but Skilled and has only built up such a large crew because he won them in games stacked in his favor, but they seem to genuinely enjoy serving under him because of the fun carnival atmosphere of the Davy Back Fights.
The Logia Devil Fruits are the rarest and give their users the most powerful abilities; Smoker, Ace, and Crocodile are among known Logia users. However, Honey Queen from the second movie (whether it was canon or not) was a Logia user who was pretty incompetent, trying to flee when her own siblings were losing, lacking the courage most Lugia users have. She didn't get far either, captured by Nami who simply bottled her up in a jar after she had assumed fluid form.
Japoli, Katejin, and Enge, the Punch Clock Villains of Overman King Gainer who are completely incompetent in their jobs, and are only a threat if they have Overman. They are the main source of comic relief with the Siberian Railroad.
Meowth as well. He is one of the weakest battling Pokemon in the series, thus spends the large majority of the time assisting with the duo's zany schemes and blabbing his mouth off rather than face an inevitable curbstomp.
Meowth had an excuse. He spent so much time when he was young learning how to talk that he let his natural skills and powers as a Pokémon degenerate. He may be a poor Pokémon in terms of battles, but being able to talk (and translate the language of other Pokémon for his two partners) does occasionally have advantages. (Disadvantages too. He was kidnapped by Hunter-J once because she felt a talking Pokémon was worth a bundle.)
Dorodoran in Futari Wa Pretty Cure Splash Star. Unlike most Pretty Cure villains, he's trying as hard as he can from the start, and is increasingly frustrated and upset by his repeated failures. When he finally comes close to victory, it all evaporates due to sabotage by Michiru and Kaoru. It's hard not to feel sorry for him.
Later, in Yes! Pretty Cure 5, Bunbee almost exactly duplicated Waspinator's history: while introduced as a serious threat, he quickly fell into this, which had the side effect of making him popular with the fans, which saved him from being killed off at the end of the season and led to him getting a happy ending in the final episode. Fortunately for Bunbee, YPC5 has no equivalent to Beast Machines.
Mousse from Ranma ˝ is a loser whose plots against Ranma go only so far before backfiring spectacularly. He's usually played as an unrepentant jerk, although maybe once a season, he'd get a moment of quiet reflection for the audience to sympathize with him — right before going back to his old ways, naturally. Both the ineffectual and sympathetic aspects are ironic, because Mousse is the most ruthlessly homicidal of Ranma's regular rivals. By contrast, Mousse spends most of the series willing to do just about anything to kill Ranma, routinely using bladed and impaling weapons and attacking with ambushes. He even comments once on being willing to slip poisonous mushrooms into Ranma's food.
Many a member from a Quirky Miniboss Squad in The '90sSailor Moon anime falls into this trope. The noteworthy examples are Jadeite from the Shittenou, Ail and En from the Maikaju filler arc, Eudial and Mimette from the Witches 5, the Amazon Trio, and both Sailor Iron Mouse and Sailor Aluminum Siren from the Sailor Animamates.
Technically though, Eudial wasn't so ineffectual and was more of a Not-So-Harmless Villain, as she staged a trap for Sailors Uranus and Neptune to get their talismans, and it worked. She got the talismans and had the the Sailor Soldiers on the ropes. The only reason she failed was because she didn't count on A: Sailor Pluto arriving, and B: Mimete rigging her brakes in order to get rid of her.
Keroro from Sgt. Frog probably counts. His schemes to conquer Earth always seem to end in disasters of some kind, when he's not being sidetracked saving the world from other alien invaders or something.
Martina, the anime-exclusive Guest Star Party Member and fallen princess from the second season of the Slayers anime, who only knows how to perform minor curses and can't defend herself at all. She spends the first half of the season trying to get revenge on Lina and her friends for destroying her home, and fails every time; after that, she decides to tag along with them. She doesdecide to help Lina out morally during the final battle, though.
Dr. Gel in Space Dandy is shown to be the devoted and apparently quite intelligent general of the Gogol Empire, under the equally competent Admiral Perry. However, the poor ape's contuinued attempts to capture Dandy often end up with him being outmaneuvered (and on more than one occasion killed) often without Dandy even realizing he was being hunted in the first place.
Subverted with Bea, when it is revealed he was actually a spy for the Jaicro Empire, who shoots Gel before turning traitor on his employers as well.
Viral from Tengen Toppa Gurren Lagann, who does not have Spiral Power like the protagonists and thus can only watch as they reach ever increasing heights of power. By the time the heroes reach the Spiral King himself, Viral, even given immortality and a four-armed upgrade to his Humongous Mecha, is swatted aside by Simon as if he is a humorous interlude.
All the villains of the Time Bokan series. The Doronbo Gang from Yatterman is the most famous example.
In the original Manga, Mokuba (who was far nastier than the one American fans know) tried to get even with Yugi with a rigged Capsule Monster game. (The rules Mokuba set down were that they would take turns using a vending machine before they started to get game pieces so neither would have an advantage; Mokuba had the machine fixed, so that he got powerful pieces and Yugi only got Com Mons.) Unfortunately, Mokuba was a Bad Liarand a bad bluffer, and Yugi easily saw through this charade and defeated him with what he had. To make this worse, Mokuba forced him into another Capsule Monsters game during the Death-T arc with much bigger stakes, using the exact same trick. A combination of overconfidence and foolish pride led to him playing sloppy - as opposed to Yugi, who had to do so carefully - and Yugi prevailed again.
Insector Haga and "Dinosaur" Ryuzaki were probably the most well known examples. You kind of felt sorry for them after awhile. Their worst humilation came during the KC Grand Prix when they dueled Zigfried two against one, and he beat them both... On his first turn. (Granted, Zigfried is a guy who gave Kaiba one of the most epic duels of his career, but still...)
Not that there weren't others. There was Jean-Claude Magnum (a Hopeless Suitor to Mai, and a Miles Gloriosus) the unnamed Rare Hunter called "Seeker" by fans (half of Yugi's dialogue during the duel consisted of "The Reason You Suck" Speech) and Gurimo from the DOMA arc. (If you've only seen the dub, that would be the first duelist seen using the Seal of Orichalcos; the dub didn't think he was worth a dub name.) Seriously, Gurimo not only used one Artifact of Doom (The Seal of Orichalcos) he was dumb enough to combine it with a second one (Obelisk the Tormentor). The only thing that was truly surprising about his loss to Yugi is why all the other characters found it so surpising!
In the first season, almost every Obelisk student shown as an antagonist except for Manjyome, Asuka, Fubuki, and Kaiser qualifies. (Clearly, most of the students there did not get to the best dorm based on merit.) Others villains like this included Seven Stars member Abidos III who was a participant of the original Shadow Duels of Egypt and undefeated - but only because his servants let him win and the Duel Spirit Don Zaloog (not a bad duelist, really, but not a good villain, he and his gang tried to steal the Shadow Gate Keys, which was pointless, because they wouldn't function unless you won them from the owners).
The second season had its share; the Alien of Light whom Judai met in Neo Space had one of the worst deck strategies ever, focusing on a monster whose Attack Score was equal to 1,000 times the cards in the user's hand. That would seem fine if not for the fact that he needed to discard two cards to summon it... And it couldn't attack the turn he did... And he couldn't draw any more cards after doing so. (Maybe justified in that he was supposed to be a Warm-Up Boss for Judai after gaining the powers of Neo Space, but it was still pathetic.)
Starting Season 3, the show took a Darker and Edgier theme and this sort of villain was rare, but there were still a couple. In Season 4, there was Sorano, another Obelisk snob who saw Judai and didn't see past the red blazer. (Some people just don't learn.) Not only that, his Horus deck seemed like it was copied from a magazine, aside from one part of the strategy that needed an anime-only card. He only became a true threat after he was possessed by Trueman.
Yu-Gi-Oh! 5D's continued the trend, but not as much. As early as the second episode there was Uryu, a hoodlum who was sent to Satellite for causing trouble, who lost a duel to Yusei because he didn't know how his own card worked. Aki had two opponents that qualified in the Fortune Cup alone, Jill deLauncebeaux, and Kodo Kinomiya (the second one a guy who bordered on Stupid Evil, seeing as he knew he was dueling a powerful Reality Warper and spent the whole duel flinging insults at her.) In the second season there was the D-Wheel thief Cid (who rigged his Death Trap so that he wouldn't fall victim to it, only to almost be done in by it because he rigged it badly) and the Loan Shark Garome. ("Oh, come on, Jack Atlas can't possibly be as good as people say he is...")
Harry Champ from Zoids: New Century, though he's more of a rival than a villain per se. Major Polta is certainly ineffectual, but does very little to garner sympathy aside from kidnapping Leena.
There's also the Zabre Fangs; though they do prove to be worthy opponents a few times in the series, they're mostly comic relief, and, in fact, lose their final battle against the Blitz Team when their Zoids do a facefault and malfunction from the fall.