Songs of Solace

Besides the usual entertainment value, people listen to music when they are feeling depressed or sad, or if they have gone through a rough time. Turning the volume up all the way helps block out the various sounds of the world around you and enables you to forget reality, for a little while at least.

For someone whose personality is based around this trope, see Headphones Equal Isolation.

This is, of course, Truth in Television.

Examples of Songs of Solace include:

Anime and Manga

In the anime Elfen Lied, during her horrible childhood, a lonely Lucy meets Kohta and spends the summer with him. One of the most notable things they did was sitting out in the rain together while listening to the song "Lilium" coming from Kohta's music box. For the first time in her life, Lucy closes her eyes and is able to forget everything terrible that's happened to her thus far, for a moment. At various points during the series she hums the song, reveling in the wonderful memories she shared with Kohta. In her words, she "was able to survive that long because she clung to the hope that she would be able to meet Kohta again someday and apologize".
In the earlier episodes of Neon Genesis Evangelion, Shinji regularly listened to Track 25 for "You Are the Only One" and Track 26 for "Blue Legend" on his SDAT player in an attempt to shut out the world. In episode 25 when the batteries finally go dead, he ignores it, which is a sign of his increased apathy.
In Puella Magi Madoka Magica, while Kyousuke is in hospital with an injured hand, Sayaka tries to cheer him up by getting him to listen to classical music. It has the opposite effect, because it reminds him that he can't play the violin any more. Later in the series, when Sayaka becomes a witch out of despair after realising she can never be with Kyousuke, she has her familiars (who look like him) play music for her.

Film

In Star Trek: First Contact, after being denied permission to take part in the defence of Earth, Picard stays in his office with Berlioz turned up full blast to the point it is causing vibrations on surfaces.
The 1989 Tony Danza vehicle She's Out Of Control had the teen protagonist lock herself in her room playing her music at full volume after a fight with her father and a breakup with her boyfriend. When one of her friends comes looking for her, she is directed "up the stairs, follow the sad music".

Literature

Edward in Twilight listens to music in his car to calm down after meeting Bella and almost killing her.
In the Lonely Werewolf Girl books, Kalix likes to listen to the Runaways loudly when she is depressed or angsty (which is to say, often). Daniel does much the same with his Goth/Death Metal music whenever he feels angry or frustrated with Moonglow (again, often).

Live Action TV

In Glee, lovesick school counselor Emma sings/cries along to Eric Carmen's "All By Myself" while sitting in her car in the rain.
Xander plans to do this when Buffy rejects him in the first season of Buffy the Vampire Slayer.

"I'm just gonna go home, lie down, and listen to country music. The music of pain."

- In "Entropy" after Xander's wedding goes pear-shaped he gets drunk listening to "Sao Paulo Rain" by Tom McRae.
- In "Forever" Giles listens to "Tales of Great Ulysses" after Joyce's death, which he played for Joyce during the events of "Band Candy".
- "Lie to Me" reveals that when her friend Ford moved away Buffy would spend hours locked in her room listening to the song "I Touch Myself". She hastens to add that she had no idea what it meant at the time.
In Angel, not only does the titular vampire listen to sad music when he's depressed, but his song of choice is Barry Manilow's "Mandy".
The Deep Space Nine episode It's Only A Paper Moon has Nog listening to "I'll Be Seeing You" loudly and repeatedly as he tries to get over his PTSD.

Western Animation

In Lilo and Stitch, Lilo slumps on the floor and listens to "Heartbreak Hotel" after being rejected by the other girls.
"Soon" is sung by Thumbelina to comfort herself because she's lonely. Her mother later sings it to comfort herself over her missing daughter.
"Baby Mine" from Dumbo is sung by Mrs. Jumbo to comfort herself and her baby because they've been separated due to the former's going Mama Bear to protect her baby.