Saved/escaped at the last moment occurances
 

This trope is typical of so much media, that I would like to see a good list on occurances in the OT/Next Mutation here, and is one of the reasons why I like the cartoons better than the comics. From the first six episodes alone we have:

TURTLE TRACKS:
-Turtles/April escape Security Services building at last second before getting drowned. (April's escape into the sewers does not count as she definately could have gotten up and ran around.)
ENTER THE SHREDDER:
-Turtles crack password before getting squished to death (happens again in the show I believe).
-Turtles destroy wall with Foot Clan missle before spike roller squishes/stabs them to death.
A THING ABOUT RATS:
-Turtles/April/Splinter escape April's apartment before getting burned to death/fall through floor.
(Interestingly, the first "failure" occured here where the Mouser Control Building collapsed on Michelangelo, but survived unscathed).
SHREDDER & SPLINTERED:
-Donatello/Leonardo escapes Krang's android body before it shrinks and crushes 'em to death
-Splinter unscrews screw, hits switch in Technodrome, frees himself from forcefield, grabs missle, runs and destroys Shredder's retromutagen gun before turning the turtles into baby-size creatures.
-Turtles escape Technodrome literally RIGHT before it gets sucked into Dimension X whereas when you first watch it, you think the turtles got sucked in, too!
RETURN OF THE SHREDDER:
-Leonardo frees Splinter right before Baxter's giant hand crushes and kills him.

Here's some more:

The Big Break In - The turtles use the Minimizer to shrink the Technodrome just as it was about to run over April.

Return of the Technodrome - Splinter gets out of the Technodrome from the hole made by the throwing star just in time as it headed to the earth's core.

Divide and Conquer - The turtles push Dregg into the portal to Dimension X just in time so Krang's body wouldn't explode on earth.

Turtle Trek - The turtles escape through the Technodrome portal just in time for the plant creature to grab it. The turtles also escaped the plant trap just in time to not get hit by Shredder's retro mutagen cannon.

Mikey's birthday... he was strapped to the Flushomatic and had mutagenic acid about to spill on him. I swear, it was mere inches away pre-commercial break, and then it was just starting to ooze out, giving him time to escape.

April almost gets killed in the Mutagen Man episode. She is tied to a rope that pulls her into moving gears. It stops a second before she touches it.

Baxter's clock-tower trap in his first CBS appearance, where it, like the Techodrome in "The Big Break-In" went by slowly and it seems they all got rescued at the last minute.

Shredder was going to cream the miniaturized Turtles with a crowbar when the news van with April and Splijter burst in.

The turtles rescued Splinter from being run over by a train and April from being destroyed inside Gorgonzola by said train. OK, the second was Zach but still.

April stopped a meltdown of a child's toy in "Invasion of the Turtle Snatchers" - by pulling oyht the batteries.

Aunt Aggie satopped Professor von Volt's Doomsday device from going off at the last second.