Ignoring by Singing

This is when a character gets on another character's nerves, usually by talking nonstop, and the other character covers his ears and starts singing so he can't hear him.

The person doing this will almost always either start singing The Star Spangled Banner, or else just go "La la la". This is sometimes done (in-universe or in real life) to avoid hearing a Spoiler, something Squicky, or anything else that a character feels he or she would be better off not hearing. Usually Too Much Information.

Examples of Ignoring by Singing include:

Fanfic

Done in the Teen Titans fic A night out:

Garfield just laughed at that. "That's what I love about you two. You're exact opposite but have such a strong friendship."
"Friend Raven is the best girl friend that I have. She even helps me during the week of blood." Said Kory with a bit too much enthusiasm.
"Too much info Kor. LA la la la." Said Garfield with his hands on his ears.

Film

Done in Dr. Jekyll and Ms. Hyde during one of Richard Jacks's attempts to explain his plight to Sarah.
Liar Liar - Jim Carrey's character knows he is cursed to speak the truth when answering a question, but not if he can't hear the question!
Miracle Max in The Princess Bride, when his wife is provoking him by reminding him of his treatment by Prince Humperdinck.
Beverly Hills Cop. After messing up the cigarette sting operation Axel Foley is bothered by fellow cop Jeffrey. Foley uses the "la la la" version while trying to get Jeffrey to stop.

Foley: I am not listening to you.
Jeffrey: Great. Real mature.
Foley: I am not listening to Jeffrey, but he's still talking.
Jeffrey: I hate when you do that.

In Honey I Shrunk the Kids, when Ron and Amy get into an argument, Ron plugs up his ears and hums "Stars and Stripes Forever". She gets back at him later by handing him a fistful of mud while softly humming the same tune.

Literature

A Dave Barry book mentions the trial of a Corrupt Corporate Executive whose defense was apparently based on the fact that he didn't know there was any embezzling going on. So the obvious procedure is to stick your fingers in your ears and yell "Lalala I can't hear what you're saying!!!" during board meetings.
In one of the Ender's Game books, Peter tells Petra that she's arguing like a nine-year-old, and that she might as well put her fingers in her ears and say "La la la, I can't hear you." Of course, she promptly does.
Septimus Heap: Merrin Meredith does this to drown out the irritating wail of a Swamp Wraith.
In the third Diary of a Wimpy Kid book, when Greg and Rowley are being driven to a roller skating rink to impress Holly Hills and Susan overhears the conversation:

Susan: Holly Hills? Holly Hills was the only fourth grader at school who wasn't potty trained.
Greg: LA LA LA...I CAN'T HEAR YOU!

Live Action TV

Played for Laughs in an episode of True Blood: One of the main characters is a psychic, and one of her friends wanted to keep a secret from her. When the psychic tunes into her friend's thoughts, all we hear is "LALALALALALALALALALALALALALA".
Invoked/Exploited/Enforced (whatever) in Bones where Booth has to talk to Brennan and Sweets about something grisley in front of his yong son, so he has his son cover his ears and sing a song while the adults talk.
Attempted by Kurt on Glee when his dad gives him "The Talk". Fortunately his dad forces him to sit and listen to what winds up being a very sweet discussion about the importance of self respect and sex.

Music

The filk band The Flash Girls turned this trope into an actual song: "A Meaningful Dialogue"

Newspaper Comics

Dilbert: H.R. Director Catbert covers his ears and sings "Pinball Wizard" whenever an employee tries to give him input.
Calvin and Hobbes: Calvin covers his ears and sings "The Star-Spangled Banner" when Hobbes tells him he'll be short all his life and his parents are planning to sell him to a sideshow.
Taken to the extreme by Paul in a Buckles Sunday strip from summer 2007, when he refuses to give his food to Buckles, who keeps begging for it by making whining voices. This was in the last two panels.

Puppet Shows

When Charlene and Robbie on Dinosaurs ask a teacher questions he doesn't want to answer he goes "La la la, can't hear you!"

Theatre

In Avenue Q, Rod tries using "la la la" when Nickie tries to discuss homosexuality with him in the "If You Were Gay" number.

Video Games

There's an NPC in Ratchet and Clank Going Commando - a biker in Vukovar Canyon on planet Barlow - that uses this trope because Ratchet offended him; he is only willing to listen to Clank.
This happens twice in Kid Icarus Uprising: Thanatos does it when Pit wonders aloud whether Thanatos is Obfuscating Stupidity or just dim, and Viridi does it when Pit comments on how the Komaytos look like Metroids (because, according to Viridi, the two video game universes have nothing to do with each other).
In The Sims 2, if two sims have a bad conversation one of them might cover his or her ears and go "La La La La!".

Web Comics

A running gag in early Arthur, King of Time and Space was Arthur doing this every time Merlin started predicting things he didn't want to hear.
In Freefall, one of the robots uses this as a "security measure" against sticky notes detailing Gardener in the Dark, an update which will effectively lobotomize every robot on the planet, and which is forced on any robot which searches the name on the network, because all they know about it is that it's so dangerous it caused one of them to open his power breaker to avoid its effects. [1]

Western Animation

This happens in The Emperors New Groove with Kuzco and Pacha after Pacha warns Kuzco not to venture into the forest. Kuzco responds "La la la la not listening" and keeps it up a bit as he starts walking on the path into the forest before "la la" ing again and shouting back "still not listening!"
Futurama, "Godfellas":

Fry: You can't lose hope just because it's hopeless. You gotta hope more, then put your fingers in your ears and go "Blah blah blah blah!"

Adam West does it at least once in Family Guy, in the episode where he made a giant golden Dig'Em statue and the town protests against this waste in taxpayer money.
In The Rescuers Down Under, Frank the frill-necked lizard covers his ears and sings "Waltzing Matilda" when Krebbs the koala starts describing what the poacher is going to do to them.
On the season nine Simpsons episode "Simpson Tide," the Naval Reserve recruiter does this when Homer tries to ask him about a question on the application that got blocked out about being a homosexual, which, if asked, would get the recruiter sent to jail for discrimination.