Animation Age Ghetto: Zig-zagged. While they haven't shown animation on a regular basis since the cancellation of the Turn of the Millennium weekly series Cartoon Alley (which featured shorts from The Golden Age of Animation, mostly MGM and Warner Bros. output) and the decision around the same time to stop using old MGM cartoons as interstitial content, the network isn't afraid to occasionally give the medium the kind of attention and respect it lavishes on live-action films — focusing on underexposed/underappreciated works to boot. (Also, with regard to animated features, bear in mind that the pool TCM has to draw from is rather small, as Disney — which until The '70s was the only studio consistently making them — keeps its films on its own channels.) Examples:
The January 2006 retrospective of the work of Hayao Miyazaki and Studio Ghibli, which featured both the English-dubbed and subtitled versions of most of their films, plus the subtitled Only Yesterday (which, until 2016, never had a North American home media release).
October 2014 had a "Back to the Drawing Board" animation marathon, highlighting some of the most important animated cartoons from The Silent Age of Animation, including the works of Winsor McCay and the J.R. Bray Studio, and even the work of obscure studios like Van Beuren. (Though like the Popeye incident above, the Van Beuren shorts were accidentally replaced with a repeat of the Winsor McCay program; the Van Beuren block was rescheduled and aired on December 7th.)
Occasionally in the off hours (late, late night or morning) they've aired Magic Boy — MGM's English dub of the 1959 anime feature Shonen Sarutobi Sasuke — in widescreen, starting years before it received a home media release (through Warner Archive) in North America.
In April 2017, they devoted an entire Sunday night block to animated shorts produced by the National Film Board of Canada from the 1940s to the '90s.
Cult Classic: TCM Underground, which has been airing late Saturday nights/early Sunday mornings since 2004 (though it, like other blocks, takes a break in February for the 31 Days of Oscar marathon to run), is a programming block that focuses on movies of this stripe. Exploitation Films, Blaxploitation films, all kinds of horror films, Unintentional Period Pieces, So Bad, It's Good movies, and just plain quirky movies all have a place here. Even the interstitial programming in the block consists of vintage shorts that would make the Rifftrax gang smile. Very likely to run films that otherwise fall under Keep Circulating the Tapes.
Rescued from the Scrappy Heap: Did this for Ted Turner, who was previously reviled by cinephiles for his enthusiastic support for colorizing old black & white films.