Squidward from SpongeBob SquarePants. When he's not keeping himself to himself, he's going around demanding people's attention by displaying interpretive dancing or playing his clarinet really loudly.
Spongebob is a more indirect example. Often he is not so much narcissistic as he is demanding of other people's company and enthusiasm, making him very clingy and completely refusing to believe anyone could not want to hang around him.
Bloo from Foster's Home for Imaginary Friends, with many storylines resulting from Bloo getting jealous of the attention received by other characters, then doing something Jerkass-ish in response. Several parts of his dialogue imply that his greatest fear is not being loved by anyone, a fear which Mac is shown to share sometimes. He probably even created Bloo for the sole purpose of having that NOT happen to him. Of course, Bloo's tries to get the others to like him backfire more than just frequently.
Most of the Drawn Together housemates fit this trope, but Toot Braunstein is far and away the worst of the bunch.
Chris from Total Drama Island definitely counts as one, it's made even funnier whenever Justin is on screen stealing the spotlight:
Chris: (to the campers who are all staring dreamily at Justin) Hey! Stop looking at the gorgeous man-candy! Focus more on me!
It's hilariously worse in World Tour. One of the teams features an Ascended Fangirl who names the team Team Chris is really really really really really hot. Chris is proud.
Stewie and Peter on Family Guy, to hilarious extremes. Meg qualifies as a more desperate and lonely version of this, though she's always played as the Butt Monkey.
Later episodes have occasionally deconstructed Brian's left wing ethics in such a manner, claiming he only supports the less popular vote because he wants to stand out and be a contrarian. He has shown to get particularly frustrated when he isn't appreciated, and has a large tendency to boast every activity he takes part in an excessive manner, even when the family are ignoring him completely.
A possible tragic example of this trope is Clay Puppington, the self-centered father of Moral Orel. This is especially apparent in the third season episode where we see his past. He thought himself the center of his mother's world, and was distraught when he learned he had several older siblings who were miscarried due to his mother's blithe ignorance of proper activities to do while pregnant (knitting: yes. going on roller coasters and trampolines: no). This caused the accidental death of his mother when he pretended to have died and gave her a heart attack. When his father ignored him after this, he deliberately and repeatedly goaded the man into hitting him, and now with his own son associates beatings with affection.
Joe is this as well.
Bender of Futurama pulls stunts all the time so that people will pay attention to him. The biggest probably being when he got a slave population to build a towering statue of him that said "Remember Me!" and then shot fire from its eyes.
"Hey! Look at my head! Look at my head! Look at my head!"
On Mom's birthday, all the robots went to celebrate with her. Bender started trying to draw her eye from the crowd, blithely yelling, among other things, "I need attention!"
Zoidberg, similar to the Meg example above, is the desperate Butt Monkey version of this.
"Hooray! People are paying attention to me!"
Another example is actor Langdon Cobb in the episode "The Thief Of Baghead". In fact, his species literally feed off it.
Kuzco from the The Emperor's New Groove/School series, which seem to be parallel continuities. The movie features Character Development, so that at the end, he becomes a very nice, likable guy. In the series, however, he still acts like a attention-loving jerk, as though the events of the movie had never happened.
Otto Rocket from Rocket Power certainly qualifies for this trope. As if being a competitive, arrogant jerk wasn't enough, he's a complete show-off who always want everyone to notice him for his skate moves. He's at his worst with this in "Reggie's Big (Beach) Break''.
Oddly enough, there's a level of Truth in Television to this, because this is how ducks actually behave. They're one of the few types of animals to walk right up to people without a hint of apprehension. They are noisy and always try to out-noise other ducks (and people). And when there are ducklings, the mother will parade them around everywhere.
Totally subverted with Wade from US Acres/Orson's Farm
Ty Lee actually plays with this trope a bit, as at the end of the series, she seems to have a bit of off-screen Character Development and joins the Kyoshi Warriors, and she doesn't care that they all dress identically.
Aang too, sometimes. Though he really just naturally finds himself at the center of attention, being the Avatar and all, and likes it there. Especially when it comes to Katara.
"Hey Katara, look what I just learned to do with earthbending!"
This has a Freudian Excuse as well. Before he ran away and got frozen, his friends were starting to alienate him for being the Avatar, and the other monks wanted to send him away from Monk Gyatso, the closest thing to family he had. Since almost all his friends from his former life are dead now, and he has an entire army of people trying to kill him, he has a niggling fear of being lonely and unloved, making him more possessive and clingy of the friends he does have.
James the Red Engine. He always wants to show that he's the best, and his accidents just seem to be a bit... more ridiculous than those that the other engines got into.
Epitomized in "Lisa vs. Malibu Stacy", where his suggestions for (unflattering) names for Lisa's doll made to compete against Malibu Stacy fall on deaf ears, leaving him desperately crying out for attention.
It's also emphasized heavily in the non-canon story in "Treehouse of Horror II":
Dr. J. Loren Pryor: The way I see it, Bart, you crave attention. Am I right?
Bart: Hell, yes!
Pryor: The problem is, you don't care whether it's good attention, like getting good grades in school, or bad attention, like, oh say, turning your father into a jack-in-the-box.
In "Treehouse of Horror VI", specifically "Attack of the 50-Foot Eyesores", the ad company executive claims this is true of the giant advertising mascots and advertisements in general, and that they need attention to live; if people stop paying attention to them, they lose their power. (And indeed, isn't that how advertising works?) Of course, it's hard for the townsfolk not to give attention to a group of monsters destroying the city, but Lisa and Paul Anka are able to convince everyone to ignore them.
Allen in Allen Gregory is this in full spades. Everything he does always has to drawn attention to himself and everything has to be about him (he is only 7 years old!) His father, Richard, is even worse; if the attention isn't focused on him, he will make it be on him, regardless who it affects.
Although normally a Genki Girl, Pinkie Pie will slip into this if anyone dares to ignore her or reject her friendship. There are two episodes dedicated to this, where Pinkie uses copious amounts of Cartoon Physics and borderline reality warping to mercilessly chase them all over Ponyville.
Played with in Equestria Games; Ms. Harshwhinny assumes Spike is one for wanting to do "something really worthy of the Crystal Empire's admiration," when he's just attempting to make up for what he sees as a failure in the torch lighting ceremony.
Ms. Harshwhinny: Next thing you know you'll be asking to put on a rock concert! Ugh, celebrities.
Quinn in Daria seems to enjoy being the center of attention a little too much.
The Equalist promoter in The Legend of Korra is said to be one, according to the official website.
Vana in Sidekick likes to be the center of attention and won't accept that some one else is getting more attention than her.
Stella is one in Winx Club. While she is a good person at heart, she always wants her friends to say how good she is. At one point she makes fake emergencies calls to her friends so that they can attend her make shift fashion show.
Lumpy Space Princess from Adventure Time is one. She even tries to crash a wedding of two people she barely knows solely to be the center of attention.
Trip Tank has a recurring sketch called Suicidal Attention Whore Chicken which is...well about a chicken who nearly kills himself just to be the center of attention.
In Jem, this is Pizzazz's primary motivation. She's a spoiledRich Bitch who wants to be famous and adored. Her violent hatred of Jem stems from the fact the Jem and the Holograms are more popular than the Misfits. Pizzazz has a Freudian Excuse behind it though. Her mother left when she was young and her father was distant growing up. The attention of fans is a substitute for the lack of affection she had growing up.
This is a big plot point of an episode of Wander over Yonder. A race of Viking-expy anthropomorphic sheep-men are being besieged by a Troll, an actual troll with all the behaviors of a dreaded Internet-troll. The troll attacks their great hall, and feeds off of the anger he incites with his insults, making him grow to enormous side. Wander doesn't even attack him, and completely blows off his insults, weakening him. Soon Sylvia and the sheep-men realize what Wander is doing, i.e., "don't feed the troll", and ignore the troll as well. He shrinks back down to the small-rodent-size he originally was and Wander simply covers him with a teacup to drown out his cries for attention.
Roger: You can't do this to me! You can't leave me here! Everyone's looking! EVERYONE'S LOOKING!
Man: Can you keep it down? No one's looking at you. We're trying to watch the skating here.
Edward from Camp Lazlo. One of the reasons they're rivals is because he's constantly trying to prove himself better than Lazlo.
The first episode of Fillmore! has a boy named Tommy who is an artist who heavily craves attention and recognition for his work. He even falsely accuses himself of a crime so he can be in the spotlight.