Here's the list as best I can compile it on my own. I'm sure there's some missing here that others can help us fill in.
From the WB Side:
The Censored 11 (and probably some more, which i hope someone helps out with)
Pinky and the Brain
Pinky, Elmyra and the Brain
Histeria!
Detention
Loonatics Unleashed
Shaggy and Scooby Doo Get a Clue
From the MGM Side:
Some of the MGM shorts were probably excluded here too
Mighty Orbots
From the HB/RS side of things we have:
Jana of the Jungle
Space Stars Finale Segments
The Puppy's New Adventures (and the specials preceding it)
Jokebook
Paddington (80s version)
Yo Yogi
The Greatest Adventure: Stories From The Bible
Rubik the Amazing Cube
The Little Rascals (This one is co-owned)
The Last of the Curlews
Rock Odyssey
The Three Musketeers (70s special version, 60s version aired regularly on Banana Splits)
(The following three only joined the roster after the Time Warner merger they were WB property not Turner)
The Abbott and Costello Cartoon Show
The Dukes
Police Academy: The Animated Series
From the based on DC comics group from any studio:
Legion of the Super Heroes
New Adventures of Batman (Filmation version)
Superman (Ruby Spears version)
From the odds and ends:
(The following three they have rights to English dub versions of only)
Marine Boy
Magic Boy
Hugo the Hippo
The Comic Strip (Tiger Sharks, Karate Kat, Street Frogs, Mini Monsters)
The New Adventures of Gilligan
Gilligan's Planet
Tarzan, Lord of the Jungle
Johnny Cypher in Dimension Zero
Things in debate:
Teen Force (Some say it aired on Toonami and Powerzone, no bumpers have surfaced)
Turbo Teen (He appeared in a bump on CN but some think the show itself never aired)
Dumb & Dumber: The Animated Series (It aired on foreign CN's but some think it did in the US too)
Trollkins (This one is skipped on a lot of online lists but people claim to have seen it)
Heidi's Song
Cyrano (HB version)
Bunnicula (RS special)
Robo Force (RS special)
The Zeta Project
The Wind and the Willows (Rankin bass version)
A few other points i'd need help on:
- Did The Popeye Show air all the segments they own. I believe they only directly own the theatrcials everything else is licensed.
- Do puppets count as animation here? If so The Hanna Barbera Happy Hour could be added to the list
- Does WB own anything Peanuts related. Warner Archive has released some. But I think they only own a few select things from them. Some stuff was licensed over the years but I have no clue which ones should or shouldn't be on this list.
One point I will make, I don't think a lot of the ones that were owned when Cartoon Network launched were deliberately snubbed. I think these are the ones that just never had prints made to be sent to Atlanta. If they had, they probably would have aired. CN was very risk taking back then. While we might say some of these look controversial, we shouldn't forget things that had some of their same "problems" did air in that period
The only one that has explicit confirmation it got snubbed was Histeria!. Samples turned down WB's attempt to get it on CN.