Demegawa from Death Note. It gets so bad that "Kira" Teru Mikami (though Light Yagami approves of his new understudy's taste and timing) winds up killing him. Considering he was The Scrappy who all sides of the Death Note fandom found annoying, his death was a massive relief.
There's also Kiyomi Takada who loves to be the center of attention.
Saki from To Love-Ru. It never works, as Lala keeps inadvertently upstaging her.
Sae from Peach Girl. This is pretty much what drives her to do everything in her power to undermine Momo because she's jealous of Momo for gaining the attention of their sought after Bishōnen classmates Kairi and Toji, and she wants to remain the most popular girl in school. In fact, she gets extremely nervous whenever it appears Momo is the focus of their classmates attention.
Mr. Satan from Dragon Ball Z. Note however that this actually works in the protagonists' favor, helping to maintain The Masquerade by claiming responsibility for acts of world-saving or alternately garnering public support for the otherwise unknown heroes. The world has never heard of Goku or Vegeta or even Krillin, but they have heard of Mr. Satan, and will follow his orders without question.
Asuka Langley Soryuu from Neon Genesis Evangelion. This is eventually revealed to originate from deeply-ingrained insecurities caused by her mother's psychotic break and subsequent murder-suicide...with the doll she called "Asuka".
Her Rebuild self is notably not this, possibly because its hinted her backstory is signifiantly different. She doesn't really seem to care if anyone pays attention to her at all (ignoring most people in school by playing a game off to the side, while series Asuka quickly made herself the star of the school) and her attempts to show off in battle are mostly to prove she doesn't need anyone's help rather than to show off.
Unfortunately, one of the characters from Bitter Virgin (Daisuke's self-proclaimed girlfriend, Kazuki) combines this with Yandere and threatens to claim rape if Daisuke doesn't date her. Later on she does try to (falsely) accuse Daisuke of rape, but fortunately no one believes her.
A creepy and very self-destructive version of this trope is Akito Sohma from Fruits Basket. The more traditional version would be Kimi.
The Luchadora Castor, a.k.a. Rachel Stanley, in Kenichi: The Mightiest Disciple, absolutely must be the center of attention of all times. If someone is receiving more spotlight than her, no depth is too low to sink to in order to steal it back. She goes as far as to listen to Ma Kensei's advice on what to do.
Yukari-sensei (No, not that one, though she might qualify too) from Nogizaka Haruka no Himitsu is a big drunken flirt. She'll often make outrageous statements to her class and express disappointment (read: throw a tantrum) if the class doesn't react as she likes or ignores her.
One of the possible interpretations of Autor in Princess Tutu. Although he comes across as a loner, he sets up a dramatic meeting with Fakir and quickly offers him his knowledge of Drosselmeyer, seeming rather giddy about the chance to get to show off. On top of that, when he runs into Rue and is instantly attracted to her, he flirts with her by... talking about himself and how great he is. He even has several cameos showing him yelling at people in the library to be quiet, and quite possibly making even more noise than the offenders were. He seems to have an inferiority complex, which doesn't help.
Mayu from Kaguya Hime often pretends to be sick and faints on the spot to get attention.
Sayonara, Zetsubou-Sensei: Probably the motivation behind Nozomu's attempts at suicide every action. There's also Nami Hito, but her Attention Whore tendencies only really show in her first appearance, in which she tries all kinds of gimmicks to gain pity and attention from her classmates (culminating with a threat of suicide). They all fail, of course.
This is pretty much proven when it's revealed that everything in Nozomu's suicide kit is designed to not kill him, and that he regularly goes to the gym to strengthen his neck to survive his frequent hanging attempts.
Nozomu: *after an attempt to save him from hanging himself nearly kills him anyway* What if I had died!?
The Millennium Earl in D.Gray-Man. In chapter 188, Road and Wisely are seen commenting on the Earl's need to always be the center of attention.
The titular character of Naruto starts out as one of these as a result of the extreme social isolation he suffered from being the Kyuubi Jinchuuriki. People would actively try to ignore and avoid him, but by acting out and playing pranks he could bring some attention his way, even if it was negative. He mostly gets over this once he makes real friends.
Panda from Shirokuma Cafe. Once he heard a magazine was coming to check out the cafe, he starts preening in hopes of getting interviewed and his picture taken. He also tries out different jobs at the zoo and returns to his original job after seeing how many compliments Llama received for portraying Panda, and has gotten angry at how much attention Shirokuma received compared to him when the gang go to the beach.
The Ax-Crazy Intention of the Abyss from Pandora Hearts certainly qualifies. She gets angry when no one listens to her, and even kills a chain because it INTERRUPTS her while she's talking. At which point, she goes psycho and starts laughing and dancing in the blood. She is conceited and vain to the point where she even tries to lure away the main character from his chain, Alice the B-rabbit, simply out of jealousy.
One Piece gives us "White Horse" Cavendish, a Bishounen pirate who was all the rage and loved every minute of it. That is, until the antics of Luffy and the rest of the Eleven Supernovas at Sabaody and Marineford overshadow him. Now he wants to kill them for making him old news. Luffy himself points out how stupid this grudge is. Even possessing a Superpowered Evil Side, normally considered a bad thing, doesn't bother Cavendish because it results in even more attention coming to him. In spite of all of that, however, he's an overall good guy, especially after Usopp saves his life, resulting in him giving up his grudge and becoming Luffy's ally.
Origami Cyclone in Tiger & Bunny (at least, the superhero persona; Ivan himself is more of the shy type.) Because his powers, while useful for more stealth and espionage-related activities, are useless in the world of theatrical heroics, he's unable to do much crimefighting on Hero TV. Fortunately, since Hero TV is as much about corporate sponsorship and Product Placement as it is fighting crime, his sponsors find a different use for him: constant photo-bombing.