As a person involved with Batman since the age of about 3 to now 19, I have experienced his world through many different mediums. Well, 3: the shows, the movies, the comics.
And seriously - no one ever writes their own shit.
Just when I think I've found something completely original, I find it copied from OR repeated by someone else.
EDIT: Some salutes are nice, and give a feel of community around the mediums of Batman, where as others are just a shame
So here is an ongoing list of where I find repetition. I'll try to keep them as short, as connected, and accurate as possible to which came first
BATMAN TAS-BATMAN FOREVER-BATMAN RIP
In "The Lost Episode," Riddler pops a brain ban thing on Batman to control his mind and take his memories, a similar ending plot to RIP. However, Batman's mind is so fucking badass that he destroys the machine, as seen in both. Also in "The Strange Secret of Bruce Wayne," Dr. Hugo Strange uses mind reading machines to discover Batman's identity. This also occurs in Batman Forever by the Riddler. Although neither of these last alterations to the plot are very dramatic.. lol.

A DEATH IN THE FAMILY-BATMAN TAS
Also in "The Lost Episode," Batman hacks at Ivy's leaf monster thing with an axe, and the animation merely shows him repetitively hitting something on the ground with a long object in the shadows, very similar outline to Jason Todd's death by Joker
BATMAN TAS-BATMAN BEGINS-THE RESURRECTION OF RA'S AL GHUL-BATMAN AND SON-BATMAN RIP-UNDER THE HOOD
"The Demon's Quest" story arch revolves around Ra's Al Ghul and Batman's fist meeting. Although Ra's is not used as a training reference as in Batman Begins, they have their sword fight, and Ra's plans on destroying civilization for it to restart. Ra's abducts a Robin in a way to get him to join in The Resurrection.. while in the episode he abducts Robin to get Batman to join, although I think he's trying with anyone who will listen.

In "Off Balance," the League of Shadows (BTAS calls them Society of Shadows) has ninjas, and plan on setting off a sonic drill thing off in Gotham. This time it is lead by Talia as well as her father such as in Batman and Son, Batman RIP, and I am sure others. The episode also features Vertigo, who comes up in Under the Hood while Jason and Bruce are fighting, similar animation and similar effects.
BATMAN TAS-THE DARK KNIGHT-BATMAN FOREVER-UNDER THE HOOD-YEAR ONE
In "Blind As A Bat," Bruce becomes temporarily blinded and is set up with a radar system to see. Batman uses similar vision in both Batman Forever and The Dark Knight, however I don't remember why he REALLY needed it in the later other than the fact that it looked pretty fuckin awesome. Actually, I don't think they needed it in Batman Forever either.

On the discussion of that fight scene - go read Year One, Batman takes out SWAT without being quite the douche.
"Blind as a Bat" also introduces technology of different cloaking for airships in which Jason Todd references to Robin I think in Under the Hood about how cool the BatPlane is because it sends out a noise-cancellation signal.
BATMAN TAS-THE DARK KNIGHT
I guess Bullock is supposed to be the traitor cop in TDK, although that's not a fair depiction. The same for Montoya and other traitor cop. Considering these were the good cops in TAS and the movies decided to ruin that? I'm hurt. Wounded, even!
BATMAN TAS-BATMAN CACOPHONY
"Joker's Wild" - a casino opens up using Joker's name, he gets pissed and breaks out to destroy it
Cacophony - Maxie/Zeus opens a casino or something using Joker's name, Joker is broken out by Cacophony, and Joker kilss a bunch of kids to get the word out. Kinda similar, or at least idea wise.

BATMAN TAS-BATMAN BEGINS
"Dreams in Darkness" - Scarecrow is going to poison the water supply with his fear toxin by using the river underneath Arkham
Batman Begins - Scarecrow is going to poison the water supply with his fear toxin by using the water pipes underneath Arkham, and Ra's Al Ghul funds it.
Can you see why I was really not impressed with Batman Begins? It took them an entire movie to do what A CHILDREN'S SHOW did in probably 2 episodes' time (if you include back story time)

BATMAN TAS-HUSH
In "Almost Got 'Em" Ivy recalls her Halloween scandal of burning pumpkins, in which the art was similar to when Scarecrow was screaming the "Hush Little Baby" lullaby. VERY short segment, but the colorings are similar and reminded me of such
DARK KNIGHT RETURNS-DARK VICTORY-BATMAN TAS-HUSH-NIGHTWING MONTHLY
"Judgement Day" Harvey decides to fight against Two-Face and develops a 3rd personality. A Nightwing monthly arch in 2009 copied this idea sort of where Dent heard of Two-Face's plan to kill Dent's former love and signed Nightwing up to defend her. This seems to happen a lot; I believe also in Dark Victory something like this occurs, as well as Hush, DKR, and in Arkham Asylum Harvey develops even more personalities by urges of the staff so he could have more decisions in his life than death or life.

HAUNTED KNIGHT-BATMAN TAS
In "Mad As A Hatter," Mad Hatter throws an Alice in Wonderland themed trap. It's complicated, I dont want to go into the whole story, and it's not supremely interesting unless you're crazy about Wonderland lore. Anyway, he kidnaps a pretty girl to make her the Alice form the book. In Haunted Knight, (the book is kinda just a bunch of mini segments) Mad Hatter kidnaps Gordon's niece on Halloween to make her pretty little Alice in his Wonderland party at this big house with a bunch of other abducted kids. Yeah, not big, and there's not much you can do with a guy with so little range when he is the only villain of a story.
THE NEW BATMAN ADVENTURES-ALL COMICS INCLUDING JASON TODD
Haha, alright, I didn't have a comic to pinpoint this on, but "Sins of the Father" episode set up Tim Drake's character to be mostly Jason Todd. Which would be all fine and dandy except for the fools of us that started reading current Batman stories wondering why Tim Drake is acting like such a nerd and this Red hood character seems so familiar. Trust me, it was very hard to connect The Resurrection of Ra's Al Ghul's Robin (my first interaction with actual Tim Drake) as being the same Robin from TNBA. VERY hard. It's been a year of rehab to understand he is a totally different character and that I made some very bad assumptions.

TNBA-NIGHTWING MONTHLY
In the first half of the 2000s decade, an issue of Nightwing had a mini fun story about Nightwing interrupting Catwoman pulling off a diamond heist where they end up working together and they have QUITE the flirtation, which she uses wanting to make Bruce jealous and Nightwing laughs his head off. Very similar situation in the episode "You Scratch My Back" as an introduction to Nightwing.
TNBA-BATMAN 3
"Over the Edge" lol. This is how I WANT them to do the next batman movie, have Bane be hired to break Batman's back and all that. Hey, if you're gonna pull from past storylines, do it right!

DARK KNIGHT RETURNS-TNBA-GOTHAM KNIGHT
An episode called "Legends of the Dark Knight" does a little salute to DKR by kids telling stories of what they think Batman is, and one kid tells a mini part of DKR and they animate in a similar style. Gotham Knight tries to profit on this by having 3 kids tell a story about it too, but they don't actually salute anyone but themselves which is what made the original episode win awards. Meh. Okay, okay; I know that Gotham Knight was made to make money, which failed because I just rented it from Blockbusters and never returned it and paid like a 4 dollar fine, but I LIKED IT. Back off!!! haha
THE LONG HALLOWEEN-TNBA
In "Chemistry," Poison Ivy's pretty monster thingy seduces Bruce and gets him to propose, while in Halloween, well, Ivy does the same thing except it's Catwoman who saves him and Ivy is the actual one who seduces Bruce. I mean, that's kinda what Ivy does. Both stories are short, and not very interesting parts in a good legacy.