Trial
Two-Face
Mad Love
Heart of Ice
Almost Got 'im

Almost Got 'im, hands down.

I don't have a single favorite, but several. In no particular order. Not gonna rate and don't have reasons why. They just are.
The Underdwellers
Two-Face (both)
The Cat and the Claw (both)
Feat of Clay (both)
The Clock King
Eternal Youth (okay, I adore Maggie! She's fun)
I've Got Batman in My Basement
Night of the Ninja (I'm a judoka, so I might be biased)
The Strange Secret of Bruce Wayne
If You're So Smart, Why Aren't You Rich?
Cat Scratch Fever (I've admired Catwoman since I was a little girl)
What Is Reality? (love the Riddler)
The Mechanic
Robin's Reckoning (I love Robin, he's super cute and I love Loren's voice)
Blind as a Bat
Day of the Samurai
The Demon's Quest (both)
Read My Lips
Honorable Mentions (no order):
See No Evil
Shadow of the Bat (both, but the way Barbara keeps saying "dork" bugs me)
Paging the Crime Doctor
House and Garden (creepy!)
Trial
Off Balance
Mad as a Hatter
Perchance to Dream
Dreams in Darkness
Heart of Steel (both)
Beware the Gray Ghost
Appointment In Crime Alley
On Leather Wings
Tyger Tyger
I Am The Night
Moon of the Wolf
Terror in the Sky
Christmas with the Joker
How about y'all?

Possibly
Heart of Silicone
(Ironic since I don't like Robots normally)
Night of the Ninja
is also good
Robin's Reckoning
was a good two parter
Flaming doesn't help your point, it engulfs it in a wall of fire no one is going try to go through.

I have
lots
of favorite episodes, but I have a top 7:
Pretty Poison
,
The Cat and the Claw
(part 1 and 2),
Mad as a Hatter
,
Almost Got 'Im
,
Zatanna
,
Shadow of the Bat
(part 1 and 2), and
Harlequinade
nya *purr

For me, it's a tie between "The Man Who Killed Batman", "Baby Doll" and "Over the Edge" (should have been a 2-part story).

My
favorite
is Christmas with The Joker but the best were probably Robin's Reckroning or Feat of Clay.

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The Laughing Fish

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There are so many good episodes. I think Heart of Ice and Perchance to Dream are both good choices, but I would give top honors to the Two-Face two-parter. The ending with Harvey scrambling on the ground to find his coin is just too much.

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Heart of Ice is usually the first to come up when discussing the best episodes, but for a lot of people, "favorite episode" is inextricably tied to "favorite character", so that will flavor a lot of the responses you get. I consider HoI to be the best episode, for a lot of the same reasons you can hear about in the audio commentary track, but I'm partial to just about anything featuring Harley Quinn.

1. Harley's Holiday
2. Feat Of Clay Pt. 2
3. A Bullet For Bullock

Dreams in Darkness - Apparently inspired the 2005 Nolan movie as the plot is much the same. I saw this episode back in 1992 and it always stuck with me.

Almost Got Im.
You killed Captain Clown, YOU KILLED CAPTAIN CLOWN-The Joker on Batman TAS

1. Demon's Quest
2. Old Wounds
3. Over the Edge
4. Robin's Reckoning
   Sent from my 13 year old P.O.S. Desktop

My favourite episode has got to be 'Heart of Ice'. Even as a kid that episode in particular left an impression on me. I remember that The Cat and the Claw Parts 1 and 2 were the first episodes that I saw of the show (on VHS) but when I saw Heart of Ice on Cartoon Network I just fell in love with the series completely and would never miss a re-run of the show.
I remember the first episode I caught a
glimpse
of the series was one of the last episodes of the original Batman TAS back in 1995 when I was 5 years old. It was 'Second Chance' - that made me wanna watch Batman Forever at the cinemas haha! And then the following year was when I properly sat down and watched the animated series, both on VHS cassettes and on Cartoon Network.
Anyway like I said.'Heart of Ice'.
This life is a preparation for heaven, hell.or both.

The Laughing Fish
HM: I Am The Night

Heart of Steel 1 and 2

Robins Reckoning, Perchance to Dream, Two Face, Clayface episodes, Heart of Ice, Jokers Favor, Strange Secret of Bruce Wayne and Old Wounds

two face and robin's reckoning are really great - the former scared the hell out of me when I was a kid. I'd like to add another two parter - shadow of the bat