Here are some of the characters you might remember:
The Teenage Mutant Ninja/Hero Turtles
Consisting of Leonardo, Donatello, Raphael and Michaelangelo, the Teenage Mutant Ninja Turtles were four turtles that turned into humanoid creatures after being exposed to a strange glowing substance. These guys loved battling bad guys and eating pizza!
Splinter is the sensei that trained the turtles in ninjitsu. He became a mutant rat after his exposure to the rats and the same substance that transformed the turtles.
April O' Neil
April is a TV reporter from Channel 6 News. She discovers the turtles and befriends them. This was after the turtles saved her from a gang of street punks.
Irma is a Channel 6 secretary girl who is introduced in Season 2. She's a friend of April O' Neil. She also ends up befriending the Teenage Mutant Ninja Turtles.
Shredder is the bad guy. He's the main arch-nemesis of the turtles. He takes his orders from Krang. He tries to do typical bad guy stuff such as trying to destroy the earth's climate. Throughout the show, he is shown as a skilled fighter who can only be matched by Splinter.
Bebop and Rocksteady
These guys were Shredder's henchman. Often portrayed as clumsy idiots who could never do anything right. These guys disappeared from the show after being trapped in Dimension X.
Krang was the lead bad guy who gave Shredder his orders. He was basically a brain without a body that used an artificial android to move about. He came from Dimension X and commanded the Technodrome, which was a huge spherical fortress (seen below).
Lord Dregg replaced Shredder and Krang after the turtles banished them to Dimension X. He was basically an alien warlord.
Here's the intro song for the show: