Well, the obvious choice would be DCAU: BTAS, The New Batman Adventures (Depending on region, this is just BTAS Season 4), STAS, Batman Beyond, JL/U and maybe Statik Shock/Zeta project if you truly want it to be complete. Plus there's four feature lengths in canon with those: Mystery of the Batwoman, Mask of the Phantasm, Batman & Mr Freeze: Subzero and Batman Beyond: Return of the Joker.
Continuity for those is:
BTAS > TNBA > STAS > JL > JLU = Statik > Beyond, however, BB should be watched before JLU as they wrap up the BB story in JLU, and Zeta Project is started during BB but ends before BB does.
I don't recall when the first 2 BTAS films occur or if it's even stated, but they occur before TNBA starts, and Mystery of the Batwoman takes place during TNBA.
Return of the Joker is last, chronologically.
Now that I've done my tangent, I'll keep going with what you actually want to know.
There aren't many other animated continuities, due to the market being so small.
There's the Watchmen Animated film, but that's just panels from the comic with an audio book over the top. Still really nice, though I can't recall if it covers Before Watchmen or not.
Scooby-Doo DTVs are all in continuity. The first four, Zombie Island to Alien Invaders, are together, then there's the rest of them which are together.
I have an autistic timeline that links up every Scooby-Doo show and film into one continuous stream, but I doubt your uncle would appreciate my 'tism.
As for the other DC animated DTVs, there's a few continuities:
As above.
Two rather good films. Superman/Batman: Public Enemies and Apocalypse.
Crisis on Two Earths and Doom are based on the JLA comics, though not actually linked. CoTE was originally the conclusion to the DCAU, but Bruce Timm got shafted hard and made a LOT of concessions to even get it made. CoTE has Mark Harmon as Superman, which is incredibly comfy to hear.
Both adaptations of TDKR. I presume they'll eventually make a 3rd one, though I haven't heard ANYONE speak about the 3rd part, even when it was coming out, so it might of sold that poorly.
All the other DC films are standalone, save Assault on Arkham which is placed along the Arkham games and Gotham Knight which bridges between Batman Begins and The Dark Knight.
Marvel has their own animated universe, but it wasn't as well-received by critics/viewers at the time, and I don't recall them really mingling with the others shows like the DCAU did.
Those shows are X-Men, Iron Man, Fantastic Four, Spider-Man, The Incredible Hulk, Silver Surfer, Spider-Man Unlimited and The Avengers: United They Stand.
They're alright, I guess. Nothing to write home about, though. Spider-Man and SM Unlimited were the best shows of those.
X-Men is not the same show a lot of anons like. That was X-Men Evolution, which wasn't in the universe and was much better.
I did some reading, and didn't know this, but apparently Marvel as two other TV universes. They're more just "were made in the same time frame". The only real one is the Marvel Anime Universe.
As I said, there's not many choices for animated universes, even less so for films.
If Genndy ever gets set free by Sony, maybe he will finally convince people to use more animation in big budget studios. He a couple people, like Paul Dini and Bruce Timm at WB Animation are the only guys who seem to care about 2D these days.