The Real Ghostbusters/Awesome

One of the strikes "against" the show is that it tended to be a bit low-key and didn't rely on BIG AWESOME MOMENTS that left people (and kids) wooping. The final battle in "The Collect Call of Cathulhu" stands as an exception, though, as does the train fight and closing the gate in "Knock Knock", and Janine figuring out a way to take care of a near-Gozer-level entity by herself tends to stick out for Janine fans.
Another is "Mr. Sandman, Dream Me a Dream". After the more scientifically-minded Ghostbusters are incapacitated, Every Man Winston realizes how to and successfully defeats the Sandman.
- And his plan gave Janine a CMOA into the bargain: after the Sandman puts her to sleep and turns his attention to Winston, we see the sleeping Janine muttering "I'm a...I'm a...I'M A GHOSTBUSTER!" Dream Janine appears in full uniform with thrower, complete with Theme Music Power-Up, and kicks the Sandman's ass along with Winston.
Show any kid with a fear of the Bogeyman the episodes "The Boogieman Cometh" and "The Bogeyman is Back". Watching Egon overcome his (relatable) childhood fears and bust the Bogeyman had to have struck a chord with many kids. It sure did with this troper.
Using a complex holographic array to fool the Headless Horseman -- now on a motorcycle -- into crossing the bridge, stopping him cold, and allowing him to be trapped was pretty freakin' sweet, too. Low key can still be awesome.
There was also the baseball episode where Winston helps a team of good spirits against the evil ones. When he hit that last pitch (hurled by a giant one-eyed anthropomorphic elephant, no less!) and sent that sucker flying into the scoreboard, shattering it into as million pieces? Woohoo!
A spirit had been slowly but surely removing Janine's humanity while making her "prettier" and "more desirable." She was literally minutes away from a full transformation when the guys show up and evoke the Power of Love. She then uses the supernatual powers of the being she had almost become to kick the spirit's ass.
Egon giving a ghost a "The Reason You Suck" Speech in "Ghostworld", infuriating him and keeping him busy while Janine and his mother free the rest of the guys from the ghost's control. At the very end, the 'busters put him down.

Egon: Checkmate!
Ghost: But you are my servants!
Peter: Sorry, big fella. It's servant's night off.

Egon's explanation on how they are going to defeat Cthulhu, followed by the Ghostbusters putting the plan in practice. Not only the explanation is scientifically sound: it can be done in reality.
The climax to "Venkman's Ghost Repllers", where the boys make a spectacular entrance to save Peter's dad from a horde of ghosts, with a kick-ass original song playing.
In "Devil To Pay," Peter gets Winston and Ray onto a gameshow to score a free vacation. The gameshow turns out to be a front for a minor demon (Dib) to steal people's souls. After a series of challenges and a near-death experience, the guys make it out alive with their souls, but without the free vacation. Peter assaults Dib, screams at him, demands the vacation and gets his way - without using a proton pack.
In "Partners in Slime," Poso (a gangster-like ghost) has Janine and Louis kidnapped to force the Ghostbusters into giving up their technology, which he can use to be in charge of all other ghosts. Three his goons go to the Firehouse to demand a surrender - finding Egon unarmed and alone. They specifically demand to see how the Containment Unit works.

Egon: And this lever opens the trap.
(the three ghosts get sucked into the Containment Unit)
Egon: And that concludes our tour.

- Egon does this a lot - in "The Thing in Mrs. Faversham's Attic", he taunts the titular specter into getting close enough to be contained in a trap.

Ghost: Your time has ended.
Egon: Not my time. Yours. Smile for the birdie. [hits lever]

In "Revenge of the Ghostmaster," the titular spook casts a spell on the Ghostbusters and Slimer that prevents any technology from working within forty feet of them. Egon and Ray, however, figure out a Rube Goldberg-like way to trap him.
In "Drool, The Dog-faced Goblin," Drool, a small phase-shifter, makes a Heroic Sacrifice to stop a much larger and meaner phase-shifter. Up to this point, Peter absolutely hated Drool and wanted to blast the poor thing. At the end, he was forced to admit he was wrong.
In "Revenge of Murray the Mantis," the boys release Mr. Stay-Puft himself in order to bring down a gigantic praying mantis. The fistfight between the titans is epic.