Oh boy, this should attract some fans.....
This was the brainstorming of comic geniuses Kevin Eastman and Peter Laird and it hilariously spoofed japanese comics and manga with a pair of turtles 
And THAT started a whole franchise by Eastman and Laird's Mirage Comics studio, and it spawned two animated series so far, the 1987 series and the current new one which is closer to the original version, and to the real fans, the 25th anniversary movie Turtles Forever serves as a big bang end to the whole franchise, especially those who were upset about the original creators being jerk sell-outs.
Anyway, i'll personally talk about the original animated series, it's got a nice storyline, but it may anger those way closer to the original mirage comics in that Splinter was a mutated Hamato Yoshi himself rather than always being a rat and Leatherhead being a stupid ignorant idiot swamp monster rather than being a calm peaceful cultured alligator, but i really haven't read the original comics and neither have my folks, and plus before the cartoon, the turtles masks were all red, Raphael's red mask was kept, but the other turtles were given different colors to distinguish who's who - for example Leonardo mask is colored blue and Michaelanglo 's mask is orange and this version gave them pupils regardless is they wore their masks or not, and the tone was a lot brighter and the animation varied after the second season, it was pretty inconsistent although Toei's work in the first season was consistent and slightly closer to the intro (which was done by TMS i believe) and A-1 Production in Season 2 was lower quality, but was much sharper......
Still, this version introduced Krang, an anthromorphic brain mutant bent on conquering the world, and Shredder is no longer seriously menacing and he is much more of a gang-bully mastering insults and is quite bumbling and silly....
There's also Rocksteady and Bebop, a warthog and a rhino, and they are the biggest wisecrackers on the show, always followed by "oh, i always wanted to say that", and the theme tune is iNDEED the TMNT defiantly, you just can't go wrong with : Heroes in a Halfshell, TURTLE POWER! - plus
it introduced the title logo and if you'd want this series without the shortcomings and want something way closer to the Mirage Comics, then look at the classic movie - that, for sure, led to the computer games (which are even better than the entire cartoon and even the comics) and is notable as Jim Henson's last project before his death.
I haven't bothered to watch the current one and if you count that Red Sky retool, than the current one, instead of knocking out an even worse theme, should've brought back the classic Heroes In A Halfshell - TURTLE POWER as in the first seven seasons......