ETA: This page is now being updated on stuff.ommadawn.dk.

Science fiction short stories featuring cats prominently. 2 persons (N and L) grade the stories from + to -.
 
David Barr Kirtley: Cats in Victory (N+) (L+)
War between animal people, who have forgotten their origin
 
Elizabeth Bear: In the House of Aryaman, a Lonely Signal Burns (N) (L)
An enhanced cat is also one of several clues in a murder case.
 
Greg Bear and S. M. Stirling: The Man Who Would Be Kzin (N-) (L-)
A not very cat-like people.
 
P. J. Beese and Todd Hamilton: The Pride (N-) (L-)
Not very cat-like man.
 
Anne Billson: My Day by Jones (L-)
Alien, as seen from the cat's POV.
 
Damien Broderick: The Beancounter's Cat (N+) (L)
A talking cat in a magical world, or is it?
 
Fredric Brown: Mouse (L) (N+)
Bill has a cat, and access to the body of a space mouse.
 
Edward Bryant: Jade Blue (N) (L)
A new invention, and a cat.
 
Arthur C. Clarke: Who's there (L+) (N)
Boring mission, into the space suit. But wait, something's wrong!
 
Judith R. Conly: Tales of a Starship's Cat (L) (N-)
The space ship gets a new cat.
 
Philip K. Dick: The Alien Mind (L+) (N)
The cat fiddles with the steering wheel of the space ship, and the man gets angry.
 
Melanie Fletcher: Lusts of the cat queen (L-) (N)
Not very much to do with cats.
 
Carl Frederick: The Spacemice Incident (N-) (L-)
Robot cat, peripheral.
 
Eduardo Gallego & Guillem Sánchez: I Thought I Saw a Pussy Cat (L-)
The computer is shutting down.
 
Ursula Le Guin: Schrödinger’s Cat (N) (L)
Thw world is dissolving; there's a cat and a box.
 
Karen Haber: On the Tip of a Cat's Tongue (L-)
Whodunit, cat not central.
 
Peter F. Hamilton: The Forever Kitten (L-)
It is not essential that the cat is a kat.
 
Robert A. Heinlein: Ordeal in Space (L+) (N+)
You can't have a space man, who's afraid of heights.
 
Naomi Kritzer: Cat Pictures Please (L)
This AI loves cat pictures.
 
Mercedes Lackey: SKitty 1, SKitty (L+)
A man and his telepathic cat in the local space port. The locals have "mice", but no "cats".
 
Mercedes Lackey: SKitty 2, A Tail of Two SKittys (L)
Establish local cat teams.
 
Mercedes Lackey: SKitty 3, SCat (L)
SKitty gets a boyfriend, but where did he come from?
 
Mercedes Lackey: SKitty 4, A Better Mousetrap (L)
8 new kittens.
 
Sharon Lee: A Matter of Ceremony (N+) (L+)
It is something very special to be bonded to a cat.
 
Fritz Leiber: Ship of Shadows (L-) (N-)
The half blind Spar works in a pub, and takes care of the new cat, Kim, who talks and chases mice.
 
Fritz Leiber: Space-Time for Springers (N+) (L+)
Cat genius analyzes the world.
 
Glynne MacLean: Vienese Meow (N) (L+)
Schrödinger, from cat's POV.
 
Anne McCaffrey: Duty Calls (N-) (L-)
Not very cat-like lady.
 
Ian McDonald: Vishnu at the Cat Circus (N-) (L-)
There are cats, but they aren't very related to the plot.
 
Sean McMullen: Mother of Champions (N+) (L+)
Big cats intervene, when humans get stupid.
 
Paul Melko: Dysfunctional Family Cat (N+) (L+)
Everybody's allergic to the wonderful cat.
 
A.R.Morlan: The Hemingway Kittens (L?)
2 bookstore cats seem very intelligent and have too many toes.
 
Andre Norton, All cats are gray (L+)
Is there a ghost, and can the cat do something about it?
 
Andre Norton and Dorothy Madlee, Star Ka'ats 1-4 (L) (N-)
2 children travel with telepathic cats to various adventures on other planets.
 
Jody Lynn Nye: Virtually a Cat (L+) (N+)
VR cats.
 
Jody Lynn Nye: Well Worth the Money (L+) (N)
A new kind of space ship is to be tested, by 3 men and 1 cat.
 
Kristine Kathryn Rusch: Chimera (L+)
Not being appreaciated as a cat is hard enough, but it gets even harder when you're more intelligent, more like a human being.
 
Kristine Kathryn Rusch: What Fluffy Knew (N+) (L+)
Only Fluffy knows about the aliens.
 
Saki: Tobermory (N+) (L+)
The talking cat also solves crimes.
 
Robert Sampson: Feline Red (N-) (L)
What to do with all them space cats?
 
Pamela Sargent: Out of place (L+)
Suddenly people can hear the thoughts of aninals. Scientists look into it, without finding an explanation (before the end of the story). Protagonish owns a cat, playing a big part, but there are also a lot of other animals.
 
Cordwainer Smith: The Ballad of Lost C’mell (N+) (L)
A cat girl, trying to gain rights for animal people.
 
Cordwainer Smith: The Game of Rat and Dragon (L+)
Our only defense against the enemy is teams of human and cat.
 
Michael Swanwick: The Little Cat Laughed to See Such Sport (L-)
Cat woman, but not central.
 
Judith Tarr: Made of cats (L+)
The aliens are invading, again; luckily there's a cat.
 
A. E. van Vogt: Black Destroyer (L-) (N-)
Not very cat-like animal.
 
Sage Walker: Hunting Mother (L+)
Half human, half cougar. Colonizing a planet. Mother is dying.
 
Ralph Williams: Cat and Mouse (L-)
There's a cat, but it doesn't contribute.
 
Robert Moore Williams: Thompson’s Cat (N+) (L+)
Space mystery from 1952, the cat saves the day
 
Gene Wolfe, The Cat. (L+)
Cat is transmogrified, and then "haunts" the place.
 
Not SF:
 
Italo Calvino: Autumn: The Garden of the Stubborn Cats
Fantasy. (The cats own a house.)
 
David Drake: Bullhead
Fantasy
 
M. J. Engh: The Tail
Fantasy
 
TCA Lakshmi Narasimhan: Clay Cast Cats
Fantasy.
 
Mike Resnick: Travels with my cats
Magic realism.
 
Kristine Kathryn Rusch: Scrawny Pete
Crime story.
 
Kristine Kathryn Rusch: Strays
Crime story.
 
Not about cats:
 
Carl Frederick: Extra Cheese for the Laboratory Mouse
No cats.
 
Carl Frederick: We Are the Cat (N-) (L-)
Schrödinger.
 
Terra LeMay: Shrödinger’s Pussy
Schrödinger.
 
Books:
 
Pet Plague 0 - Altered Humans
 
--
 
Feel free to leave a comment, if you know of any others.