Best know for the 80's cartoon show and series of 90's live action films, they started out in a much darker origin than their kid friendly animation lets on.
The Turtles were created by Kevin Eastman & Peter Laird in 1984 and first appeared in a comic book published by Mirage studios. The actual creation of the turtles was (now famously) due to the two friends going out for dinner and a few beers, which led to Eastman drawing some half-cut ideas onto a napkin - a rare case of where the drunken "That's a great idea!" mentality actually paid off.
The comics (1984)

This is centred around the adventures of four turtles who had been mutated into anthropomorphic beings by a mysterious ooze called mutagen. They were found by Splinter, once pet rat to Ninja master Hamato Yoshi who had fled to New York. After his master was killed by "The Shredder". Splinter sought refuge in the sewers and found the turtles who had been discarded as unwanted pets. The animals came into contact with cracked can of mutagen ooze which mutated whatever it came into contact with into the last thing that it touched. He set about training his four turtles in the ways of the shadow which he had learned from watching his late master Yoshi. The team must fight their nemesis - the ninja master Oroku Saki, who goes by the persona of 'The Shredder' - master and Sensei to The Foot Clan of Ninja. The Turtles themselves took their names from Italian renaissance painters as given to them by their rodent master.
Mirage
The first comic book debuted in 1984 at a comic convention in New Hampsire. The early editions had some noticeable features that were different from more well known future incarnations. The content was considerably darker, and often times much more violent than what is interpreted today. Appearing at first in monochrome (only adding to the dark nature of the feel) and then later in slightly muted colour with all four turtles wearing red bandanas.
The comics were originally a parody of other comics at the time. Most notably, Daredevil. Daredevil's origin was of a man who was hit in the eyes with a mysterious chemical which fell off a truck, and went on to battle a Ninja clan known as "The Hand" by being trained by his master - Stick.
The Turtles origin was from coming into contact with a chemical which fell, off a truck (and bounced off a man's head), and they went on to fight a Ninja clan known as "The Foot" by being trained by their master - Splinter.
Teenage Mutant Ninja Turtles Adventures
Teenage Mutant Ninja Turtles Adventures was a comic book series published from August 1988 to October 1995 by Archie comics.. The comics stayed closer to the '87 cartoon series, but with the fifth issue Eastman and Laird decided to hand the series over to Mirage Studios employees who immediately abandoned the animated series adaptations and took the title in a different direction with all-new original adventures.
Dreamwave
Told from the perspectives of April, Baxter, Casey, and a pair of New York City police officers this monthly comic was inspired by the 2003 TV series and ran from June to December 2003.
IDW
In April 2011, IDW announced that they had acquired the license to publish some new collections of Mirage comics.The first issue was released on August 24, 2011. Turtles co-creator Kevin Eastman and Tom Waltz were writers, with Eastman and Dan Duncan handling the art duties.
Licensing agent Mark Freedman contacted Eastman & laird about a potential toy line for their characters. This led to the darker nature of the comics being toned down for the toys due to being aimed at children, and talks began to appear with Murakami-Wolf-Swenson animation studio and Playmates Inc. toys to produce a tie in animated show. It was this stage where familiar taglines (mostly famous from the cartoon) started to appear such as 'Heroes in a half shell'.
The Cartoon Show (1987)

The show also had a talented voice cast too, most notably the late great James Avery who voiced Shredder, and who was also famous for playing Uncle Phil in seminal 90's sitcom The Fresh Prince of Bel-Air.
I did a run of the cartoon not long a go, and I was shocked and surprised as to how well it stands up.
Make no mistake though, this is undoubtedly a kids show, and as such has monumentally goofy parts with rather thin plots. However, even as an adult there is still much to enjoy here. The artwork and animation are still absolutely beautiful, and with a little suspension of disbelief, the episodes flow extremely well and do press the chuckle button on morel than one occasion.
Of course nostalgia plays a huge part, but even as a historical and cultural slice of the time it can be enjoyed by keeping an reasonably open mind.
The show was broadcast here in the UK by the BBC and is now famous for early PC pandering by removing all mention of the word 'Ninja' from the show. At that time, anything relating to the Ninja phenomenon was extremely taboo thanks in part to the Mary Whitehouse video nasty movement and the genetic disposition of being British by automatically despising anything that's remotely fun or popular elsewhere in the world. Any scenes with Michaelangelo's nunchuckus were also removed becasue you know, it's a much easier weapon for a child to make than say a Bo Staff which is basically a f***king broom handle!
The show lasted a whopping 10 seasons before Turtle fever ran almost completely dry and scurried back to the shadows to lie dormant. However, no-one can deny that it's right here where the franchise was made the phenomenon that it is today, and rightly so!
7/10 (Maybe 8 if you have a particularly childish mind)
The Second Cartoon (2003)

The most notable change to the series is that there are now multiple incarnations of The Shredder which appear in this universe - the main antagonist being Ultrom Shredder. Ultrom Shredder is an alien named Ch'rell from the planet Ultrom, and has an appearance similar to that of Krang from the 1987 series who wears a mech suit which resembles the classic Shredder. Ultrom Shredder also created the Cyber Shredder who iis a digital recreation of himself.
The original Shredder, Oroku Saki, exists in this universe as Tengu Shredder, who is a demon that has possessed Saki but was ultimately defeated by the Turtles with the help of the spirit of Hamato Yoshi,
The series is often considered to be the best animated incarnation of the franchise as it largely does away with the more child friendly nature of its 1897 counterpart. However, it still retains many of it's characteristics.
Being twenty-five years old when it debuted, I was either too busy playing guitar or being drunk to have had the urge to check it out, but a recent viewing has left me pleasantly surprised with the content and quality.
Fully enjoyable for both children and adults, and a very noble era in the franchises history.
The title music is cancer inducing though, but don't let that put you off!
8/10
The CGI Series (2012)

The show debuted in 2012 on Nickelodeon and broke the mould for a Turtles TV show by being fully 3D rendered CGI. It was met with positive reviews from viewers, and even won an award for outstanding voice casting. The series does feature some exceptional talent, most famously Sean Astin of Goonies and Lord Of The Rings fame who makes an appearance as Raphael.
The series sees a few minor changes, such as April O' Neil being a 16 year old daughter of a scientist instead of a twenty-something news reporter, and Krang is now referred to as Kraang.
The show also takes from previous animated lore, such as Splinter is a mutated version of Hamato Yoshi himself instead of his pet rat (a feature from the 1987 cartoon)
The show is is currently past it's 4th series and has been an overwhelming success in introducing the Turtles to a new generation. Having only seen a handful of episodes I can only give an initial opinion, but I can say that it's very well done, with a nice mix of humour and action which doesn't get overly goofy.
8/10