Here are my 10 favourite moments from the series which lasted 4 seasons. Note there are spoilers within:
10. Cameo by Nightwing
In the episode "Grudge Match" various members of the League descend on Bludhaven to stop an superpowered fighting match. The creators didn't have access to the Nightwing/Dick Grayson character, so they couldnt include him in the episode, but an very familiar hero is seen watching over the city from the dark.
9. The Flash speeds up his heart to make it look like he is flatlining
The League is captured by a League from an alternate dimension who have decided to take the law into their own hands on their world, and aim to do it to both worlds. Batman contronts Batman and realizes he won't be able to escape because they essentially share the same mind. Wally fakes his own death by speeding up his heart so fast that it looks like he has flatlined. When the alternate Batman goes to help him he escapes and frees the others.
8. The Question finds out Baskin-Robbins has been lying to us
The Question in this series was kind of a strange character. He was more based off of Rorschach from the Watchmen than he was from the DC hero. But Rorschach was based off the Charlton Comics Question, which DC owns the rights to. He suffers from apophenia in this series unlike the DC version (apophenia is a condition where people find links among unrelated pieces of information and synthesize them together.) in one of the comedic highlights of the series, he discovers that Baskin Robbins has 32 flavours.
7 Batman vs. Doctor Destiny
Dr. Destiny: I'll be able to go into your brain even if you're wide awake
Batman: My brain's not a nice place to be
6. Wonder Woman fights the other females
Some of my favourite DC characters (al female) are brainwashed into fighting each other. They eventually break free of the control only to find Wonder Woman still under control ready to fight them all.
5. Implied interrogation by Batman
Batman captures an aperative from the country of Krasnia. The operative tells him in Krasnian that Batman can't understand him and even if he could he woudn't say anything.
4. Superman lets loose on Darkseid
Superman describes how he always has to hold back in the series' final episode, but then explains to Darkseid he doesn't have to hold back against him and then shows him who's boss.
3. Lex Luthor and the Flash switch bodies
In the series' funniest episode Flash tries to avoid being discovered inside Luthor's body and does such "evil" things like not washing his hands after going to the bathroom to play the part.
2. Wonder Woman's crush on Batman in Kid's Stuff
A romance between the two is hinted at throughout the series, but when they are tranformed into child version's of themselves, the flirting becomes a lot more obvious.
1. Batman pilots the Watchtower onto the Thanagarian hyperspace bypass and saves the planet
This is why Batman is so beloved by fans. He does what none of the superpowered heroes could do and saves the day, even sacrificing his own life (though he is saved at the last moment.)