I decided that I absolutely need a playlist of cat songs.
What I’ve got so far:
Tiger Feet by Mud
The Cat Crept In by Mud
Teddy Bear by Elvis (“I don’t wanna be your tiger, cuz tiger’s play too rough, I don’t wanna be your lion, cuz lion’s ain’t the kind you love enough”)
And a few obvious ones: Anything from the Cats soundtrack (possibly minus Memories), and anything from Thundercats (I have all the character’s theme music. 
)
Year of the Cat, by Al Stewart
Love Cats by The Cure
Well, there’s this one:
“What’s New Pussycat?” Tom Jones
“Cat Scratch Fever,” Ted Nugent
“Stray Cat Blues,” The Rolling Stones
“Cool for Cats,” Squeeze
“Cat’s in the Cupboard,” Pete Townshend
“Bear Cat (Answer to the Hound Dog),” Rufus Thomas
“Mean-Eyed Cat,” Johnny Cash
“Black Cat,” Janet Jackson
“Leave My Kitten Alone,” Little Willie John
Jethro Tull: “…And the Mouse Police Never Sleeps,” “Hunt by Numbers”
Ian Anderson: “Rupi’s Dance,” “Old Black Cat”
Gentle Giant: “Black Cat”
The Stray Cat Strut - The Stray Cats
I Am a Cat - Shonen Knife
Catnip Dream - also Shonen Knife
Yet more Shonen Knife - Punk Animals (one of the two animals in question is a cat…the other’s a cow) (That song has one of my favourite puns.)
If you can endure the…iffy aspects… The Siamese Cat Song - Lady and the Tramp
One not in English (and terrifyingly cute, as anime themes often are), but very much about cats (a good half the song is just listing cat breeds!):
Neko Nyan Dance - Harenchi Punch
“CHA!” Said The Kitty" by Local H
“Kitty” by Presidents of The United States
“LAYD” by Lions At Your Door
“Black Cat Bone” by Laika
“Gold Lion” by Yeah Yeah Yeahs (I like the diplo remix)
I love tha’ Pussy- Alpa Chino
A Great man once said,
“Now do the bunny hop! ( Turn it up!)
Crank that kitty cat! (Hey!)
It’s the ghetto’s thing!(Ho!)
With the noodle leg! (Do it, do it, do it!)
Now do the noodle legs! (Snap!)
Now do the noodle legs! (Yeah!)”
I came in here to mention “Stray Cat Strut”, but Tengu beat me to it, so here’s something no one else will think of (unless CoBa is around, perhaps):
“Swing a Cat”, from the Corsairs Black album. An a capella pirate crew singing about cats saving their ship from rats. (sample)
And I’m amazed nobody beat ME to it, given that 5 people got in in front of me.
Either it’s a miracle, or vaguely depressing. >_>
Cats in the Cradle
REM - Star Me Kitten
Elton John - Honky Cat
Lion Sleeps Tonight
Survivor - Eye of the Tiger
and just for the lols - Kitty Cat Dance and the Mean Kitty song
Special Secret Song Inside-- Red Hot Chili Peppers
Yeah, he beat me to “Catnip Dream”, too.
Something for Cat from Breakfast at Tiffany’s
Tommy the Cat - Primus
Cat DNA - Ozric Tentacles
Cat Food - King Crimson
Schrodinger’s Cat - Tears For Fears
Tigermoth - Steve Hacket
Tiger in a Spotlight - ELP
Rubberneck Lions - Oysterhead
Rammstein - ‘Pussy’
I bet you could even make a Broadway musical about Cats . . . .