Way back in the 90s, way before the Marvel Cinematic Universe was a flicker in anyone's eye, DC beat them to the punch with their own shared universe of popular animated series and films, generally referred to as the DC Animated Universe (which likely inspired the name of Marvel's later shared universe). The franchise began with the award-winning Batman: the Animated Series in 1992 and concluded with Justice League Unlimited in 2006 and proved to be deeply, wildly influential, to the point that often these versions of the characters and their stories are considered the definitive versions (sometimes more so than even the original comics). Many beloved characters and stories, including Harley Quinn and her backstory, originate here.
Like my other viewing guides for the MCU and for Doctor Who, this is a breakdown on how to watch and enjoy this franchise in the most straightforward, easy, and enjoyable order (from my subjective perspective). It will take into account chiefly release order, but also factor in narrative flow and accessibility. It will also make mention of egregious cases where episodes were aired (and thus released) out of order.
Without further ado:
Batman: The Animated Series Season One (Television, 1992-1993)
Developed by Bruce Timm and Eric Radomski. Released on DVD as Batman: The Animated Series Volume One and Volume Two. The animated short (which can be found online) "The Dark Knight's First Night" serves as a pilot to the series, and the inspiration for the series' iconic opening sequence.
Batman: Mask of the Phantasm (Film, 1993)
Directed by Eric Radomski and Bruce Timm. Its place in continuity with regards to the earlier season is foggy (Robin is nowhere to be seen, but then that is often the case even in other episodes of the show). It details Batman's origin via flashbacks, so some would place it before season one, but the tone and animation quality are more in line with later episodes.
Batman: The Animated Series Season Two, aka The Adventures of Batman & Robin (Television, 1994-1995)
Released on DVD as Batman: The Animated Series Volume Three. As stated above, is a partial re-branding of the series that emphasizes Robin as a supporting character.
Batman and Mr. Freeze: SubZero (Film, 1998)
Directed by Boyd Kirkland. Released in '98, but produced earlier and uses the art style of the original Batman: The Animated Series rather than the redesign seen in contemporary installments, which coupled with some minor character details seems to place it about here.
Superman: The Animated Series Season One and Season Two (Television, 1996-1998)
Developed by Alan Burnett and Paul Dini. Season two (and later season three) aired as part of a programming block with The New Batman Adventures called The New Batman/Superman Adventures, and features a crossover with TNBA ("World's Finest," also released as a stand-alone film) that works well as an introduction to said series.
The New Batman Adventures (Television, 1997-1999)
Developed by Bruce Timm and Paul Dini. Released on DVD as Batman: The Animated Series Volume Four. Serves as a major retool to the prior series to accompany the change in network, with an adjusted premise focusing on the "Bat Family" of characters (Batman, a new Robin, Nightwing, and Batgirl) and an overhauled art style meant to match the more stylized look of Superman. Features a crossover episode with characters from Superman. The Christmas episode "Holiday Knights," which is placed first on some releases, takes place and should definitely be watched later, at least after the episode "Growing Pains."
Superman: The Animated Series Season Three (Television, 1998-2000)
Features multiple crossovers with characters from TNBA.
Gotham Girls (Web, 2000-2002)
Written by Paul Dini and Hilary Bader. A Flash-animated web series spin-off of TNBA focusing on the female supporting cast and villains. Non-essential to the overall narrative; features writers and voices from the original series, but the rudimentary animation might be off-putting.
Chase Me (Short, 2003)
Directed by Curt Geda. A short released alongside Batman: Mystery of the Batwoman set during the time of TNBA.
Batman: Mystery of the Batwoman (Film, 2003)
Directed by Curt Geda. Released much later, but meant to serve as a finale to TNBA and to bridge the story gap between said series and Justice League.
Batman Beyond Season One and Season Two (Television, 1999-2000)
Created by Bruce Timm, Paul Dini, and Alan Burnett. Set in the distant future of the rest of the DCAU, but thanks to time travel shenanigans in later shows still needs to be watched here. The second season episode "Zeta" spins off into The Zeta Project.
The Zeta Project Season One and Season Two (Television, 2001-2002)
Created by Robert Goodman. A spin-off of Batman Beyond. Season one features a crossover with Batman Beyond's third season, released on the same day as said series' crossover episode.
Batman Beyond Season Three (Television, 2000-2001)
Crosses over with Zeta as noted above. Introduces the Justice League Unlimited of the future, setting a precedent for the later Justice League series and its sequel series.
Batman Beyond: Return of the Joker (Film, 2000)
Directed by Curt Geda. Released during season three, but can be watched after finishing the season just fine.
Batman Beyond (Short, 2014)
Directed by Darwyn Cooke. A short celebrating Batman's 75th anniversary, featuring the art style and voices of the Batman Beyond series. Can safely be assumed to be a canonical installment, even if it is a bit silly and released way after the DCAU ended.
Static Shock Season One and Season Two (Television, 2000-2002)
Created by Dwayne McDuffie. Initially a separate project from the DCAU, it was folded in when season two featured a crossover with TNBA.
Justice League Season One (Television, 2001-2002)
Created by Bruce Timm and Paul Dini. Is to the DCAU what the Avengers films are to the MCU. Note that on some releases (thanks to a late air-date) the episode "Injustice for All" is placed incorrectly. The episode should follow the episode "The Enemy Below." While differing production orders and air-date orders are common in the DCAU, this is the only one that actually messes up the story. If you are concerned about watching other episodes out of order, check out the episode orders given at worldsfinestonline.com.
Static Shock Season Three and Season Four (Television, 2003-2004)
Features crossovers with TNBA, Batman Beyond, Justice League, and Superman.
Justice League Season Two (Television, 2003-2004)
Justice League Unlimited Season One through Season Three (Television, 2004-2006)
Sequel series to Justice League. Features crossovers with Static Shock and Batman Beyond, serving as a fully absorbed finale to both series as well as the DCAU as a whole.
Tenuous Installments
These shorts, series, films, etc. have some connection to the DCAU, but for one reason or another cannot be confirmed as an official part of it.
Lobo (Web, 2000)
A Flash series in the vein of Gotham Girls. Is often treated as a part of the DCAU, but has a wildly different art style, a different actor voicing Lobo, and a reliance on graphic violence and juvenile sexual humor that sets it apart tonally.
Teen Titans (Television, 2003-2006)
Created by Glen Murakami. Not officially a part of the DCAU (with a story that does not quite match up and a wildly different tone and art style), but there are some indications of possible connection (which would make this series a prequel set some time prior to Batman). These include an offhanded mention of "the Titans" in Static Shock, and an appearance by a younger version of Wally West in Teen Titans, with the same personality and voice actor as in Justice League (though note that different iterations of the DC franchise sharing VAs is quite common). Official word from the creators is pretty flip-floppy on this.
Superman: Brainiac Attacks (Film, 2006)
Directed by Curt Geda. Released as a tie-in to the live action film Superman Returns. Definitely not canon to Superman: The Animated Series due to very different depictions of some characters (Lex Luthor in particular hewing much closer to his movie counterpart), but uses identical character designs and many of the same voice actors and is also directed by a veteran of the DCAU's own straight-to-video films.
Legion of Superheroes (Series, 2006-2008)
Created by Amy Wolfram. The show's canonicity to the DCAU is flip-floppy in a similar manner to the above Teen Titans, with which it shares a character designer. Like Titans, the art style and tone are very different, but nothing in the canon actively contradicts that of the DCAU and some elements are very similar, such as the portrayals of Brainiac, so it is really up to the individual viewer.
Justice League: Crisis on Two Earths (Film, 2010)
An installment of the DC Universe Animated Original Movies direct-to-video line directed by Lauren Montgomery and Sam Liu. Officially not a part of the DCAU (and featuring a slightly different Justice League line-up), but based on an unused script for JLU by Bruce Timm. It is at least very tonally similar to the DCAU. Many other films in the line, such as the earlier Superman: Doomsday and the later Justice League: Gods and Monsters, also feature art styles that are clear homages to Timm's designs (with Gods and Monsters being co-created by Timm) and the return of veteran voice actors from the DCAU.
Batman and Harley Quinn (Film, 2017)
Another DC Universe Animated Original Movie directed by Sam Liu. This one was written by Bruce Timm and features the same art style and many of the voices from the DCAU. Timm claimed in early interviews that he intended this film to be a part of the DCAU, but inconsistencies in the film and some backtracking in later interviews leave the status foggy.
Justice League vs. The Fatal Five (Film, 2019)
Directed, again, by Sam Liu. Like the above film, this one features a script by Bruce Timm and carries his distinctive style and is considered, by Timm at least, to be an official installment of the franchise.
And then, of course, there are a slew of tie-in comics and video games which I am not going to cover here. Many of the comics are of high quality and influenced the DCAU and wider DC universe in their own right (for example, Harley Quinn's now-famous origin story originated in one of these comics). The same cannot be said of the games; many of the DCAU video game tie-ins are notoriously considered some of the lowest-quality games in the history of the medium.