One of the common criticisms of Infinite Crisis was that it was continuity porn in both senses of the term. DC in general is perceived to engage in 'hard continuity' (i.e., inconsistencies are deliberately explained) versus Marvel's 'softer' kind (inconsistencies, especially bad ones, are eventually just ignored).
Crisis on Infinite Earths may well be the Ur-Example. DC Comics explicitly hired a guy to read and take notes on every single comic book DC had ever published as a consultant for Marv Wolfman and George Perez.
52 veers into the second variety of continuity porn, though that might depend on whom you ask. In its defence, though, it is hard to do a yearlong series touching on every character in the DC Universe without getting a little esoteric sometimes.
This was even commented on by one of the writers (Mark Waid), who mentioned that "... no good fiction ever came out of worrying first and foremost whether its events fit into 'continuity'."
Alan Moore's League of Extraordinary Gentlemen is assuredly the ultimate embodiment of this trope, being continuity porn for all continuities ever. Many sequences and moments in the stories seem to have no purpose other than for Moore to reference as many fictional places and characters as possible. To the extent of explaining Hyde's slow transformation from human to monster, and having a very small date range for the actual events (1891-1894, during Sherlock Holmes' supposed death after falling off a cliff with Moriarty. It is actually considered one of the Holmes sub-works despite Holmes appearing only briefly in a flashback).
Roy Thomas's All-Star Squadron is the best example, often going to great lengths to "solve" continuity problems that nobody but Thomas even knew existed.
In Pre-CrisisBronze Age comics, DC's guy in charge of Superman continuity was Promoted Fanboy E. Nelson Bridwell. Bridwell adored the minutia of the Superman mythos, and whenever he personally penned a story, it was chock full of Continuity Nods, often to obscure Silver Age stuff. In stories focusing on the history of the character and his world (such as the original, pre-Crisis The Krypton Chronicles and World of Krypton (1979) miniseries), this worked very well, but in stories that were set in the present day, the constant references did sometimes feel intrusive.
All-Star Superman: There's a mess of references to old Silver Age and Bronze Age stories, practically to Continuity Porn levels. Morrison's seeming favorite is the scene where the Kandorians fly from Superman's outstretched hand, a clear visual reference to Superman #125, a boyhood favorite of Morrison where Superman gained the power to shoot a tiny version of himself from his hand.
DC Rebirth by definition has to indulge in this, but the mother of all examples appears at the end of New Super-Man #8: the reintroduction of Ching Lung, the first ever villain published by DC Comics, drawn precisely how he appeared on the front of Detective Comics #1. Even the layout of the TEXT is the same as Detective Comics #1.
JLA: Year One and JLA: Incarnations were both written to show how the Justice League's history "really" happened in the Post-Crisis universe. It helped that both focused on the characters' personalities and interactions rather than harping on minutae, however.
Batman: Anytime an artist is directed to show a wide shot of the Batcave, this inevitably happens. Older versions of the Batmobile, artifacts from cases, etc. (Especially the eight-foot-high penny, the mechanical Tyrannosaurus, and the oversized Joker playing card hanging from the ceiling).
Wonder Woman (1987): For better or worse, Jimenez was very, very big on reviving anything and everything from older Wonder Woman stories, from the downright goofy (Villainy, Inc.) to the genuinely breathtaking (Themyscira II draws on resources from a half-dozen corners of the wider DC Universe).
James Robinson's Starman is perhaps the poster child for continuity nods in DC comic books. Notably, not only does Starman rely on the greater DC canon, but it has its own strong internal canon as demonstrated in the last few arcs, wherein every Checkhov's Gun is set off.