The world's smallest violin
To be sure, there are any number of actual, real very tiny violins, playable or not, that may vie for this title. But this entry is not for any existing violin, but only for a metaphorical one. The "world's smallest violin" is a phrase used in a sarcastic manner to dismiss someone else's troubles as imagined, minor, or exaggerated.
Typical use would be accompanied by a hand gesture of rubbing the tips of the thumb and forefinger together in tiny circles and asking "Do you know what this is?" And then replying that's it's "The world's smallest violin and it's playing just for you!" Sometimes, a real or invented song title is inserted, depending on the user's creativity. Sometimes it's "the saddest song in the world" or "the world's saddest song."
The metaphor assumes deep cultural familiarity with non-diegetic music - film/TV scoring. But enhancing sad scenes with violin music surely predates the existence of television and film.
Likely this metaphor evolved from previous, more generic expressions like "Break out the violins" and/or miming playing a regular violin. The violin tune "Hearts and Flowers" (composed by Theodore Moses-Tobani, published in 1893) was used so often in the silent film era it became shorthand for overdone schmaltz:
Our use of the word "melodrama" to mean a kind of hammy theatre comes from the hammy nature of what musical melodrama usually is. That is to say, mama is dying, and the landlord is coming along somewhere with a mortgage, and there are a couple of guys down in the musicians' pit playing "Hearts and Flowers."
-Thompson, Virgil. "Composing for the Movies," National Board of Review Magazine. Vol. 16, no. 1, January 1941, page 6.
Here's an early use in print from the 1958 novel The Detroiters by Harold Livingston:
"We will now hear the playing of the smallest violin in the world." "You did have a lot of talent," Frank said. "Once." "You're repeating yourself." "I've seen lots of talent come in our shop, and other shops," Frank said.
Author Stephen King used the the same variant of this metaphor in two of his works, 1982's Different Seasons:
I rubbed my first finger against my thumb. "This is the world's smallest violin playing 'My Heart Pumps Purple Piss For You,'"
And much later in the 1997 novel The Dark Tower IV: Wizard and Glass
Eddie held up his right hand. He rubbed the thumb and forefinger together.
"WHAT DOES THAT SIGNIFY, FOOLISH CREATURE?"
"It's the world's smallest violin, playing 'My Heart Pumps Purple Piss For You,'" Eddie said. Jake fell into an uncontrollable fit of laughter.
The metaphor has successfully transitioned from oral folklore to Internet memes.