Organ music ninjas! The very worst kind!
This isn’t the one you’re thinking of, but Toccata and Fugue in D Minor is also a staple of the Famous Creepy Organ Music genre.
It is, actually, I just conflated the bit about 30 seconds in with the opening in my head.
Didn’t part of Devil in the White City deal with the writing of that? It was the person who put together the Midway.
ETA: Opps, my mistake. I meant the “There’s a place in France…” melody.
Grieg’s most cliched work has to be “In The Hall of The Mountain King”
I count 45 uses in film and television alone on this wikipedia page.
That’s the one! Here’s a link to a video so you can all go, “Oh yeah! That song!” 
Another very familiar, clichéd song - Solsbury Hill by Peter Gabriel. (Music starts at around 0:50.)
Does anyone know the name of that theme with kettle drums that plays in old Westerns when the Indians come on the scene? “DUUMMM dum dum DUM dum dum dum”?
I might have The Ultimate Grieg Cliche: lisiate’s list has ELO covering ITHotMK, however, they start that version with a short bit from MM. Jeff Lynne must have been on an EG binge that week.
For when the magician or tightrope walker is performing, Over the Waves by Mexican composer Juvenitas Rosas.
Is “Sabre Dance” still a cliche, or has it been retired to Cliche Parnassus?
There are many Gypsy themes…
The quintessential sad and poignant one: https://www.youtube.com/watch?v=xir-5oAWxXE&feature=youtu.be&t=4m45s
I have a couple of Raymond Scott collections, and my impression from liner notes is that he wrote Powerhouse and most (all?) of his other pieces years before his publishing rights were sold to Warner Brothers. I’m too lazy to look any of this up, and agree to be wrong if I’m wrong.
I now think of it as “Gonna Tell Us All about the Rain.” 
Music starts here at about 1:35:
When there’s a party at a country club or some similar high society gathering, and they want to convey just how sophisticated everybody is, you often hear Vivaldi’s Spring.
You mean “The Ed Sullivan Show’s Plate-Spinner’s Theme”?*
The Nokia ring tone, which is played world-wide at least twenty times per second, is actually the Francisco Tarrega “Gran Vals”. Listen at 0:11.
Yep, the very one–HEY! I can’t be watching this; I’m getting ready for bed. That’s worse than coffee. 
Not certain if this has become “cliche” as of yet but this Miserlou from Pulp Fiction:- YouTube
Is actually a variation of this Greek song:The original Misirlou - Μισιρλού (Τέτος Δημητριάδης -1927) - YouTube
This is certainly cliche at weddings, and I would think heraldry movies (and Masterpiece Theatre), as well.