Leatherface

First appearance: The Texas Chainsaw Massacre (1974)

A group of annoying kids run afoul of a Texas family with a strange BBQ recipe. Screaming ensues. There's really not much more to the plot than that.

Some folk consider it a classic of the genre, sadly I'm not one of those people. I prefer the later entries in the series. Although I don't think you are supposed to Enjoy Texas Chainsaw Massacre so in that case it might be the most effective of the Chainsaw flicks.
The franchise has become one of the most convoluted of the Classic Slasher Franchises (Halloween, Friday the 13th, Nightmare on Elm Street, Child's Play) with numerous restarts prequels and remakes. This is how the franchise looks as of August 22, 2014:

• The Texas Chainsaw Massacre (1974)
• The Texas Chainsaw Massacre 2 (1986)
• Leatherface: The Texas Chainsaw Massacre III (1990), considering the end of Chainsaw 2 this could be a reboot although it does have a 3 in the title...
• The Texas Chainsaw Massacre: The Next Generation (1994) Probably a reboot, the only character from the first one in this is Leatherface although he behaves a little differently than in the previous movies and there doesn't seem to be any cannibalism.  It stars Matthew McConaughey and Renée Zellweger. It's got a weird Illuminati storyline explaining that maybe the Sawyers are controlled by some kind of shadowy organization. I like to pretend that McConaughey's character in True Detective is the same guy he plays in this movie only here he's in deep cover and that's why Rust Cole so conspiracy minded in TD. But I digress...
• The Texas Chainsaw Massacre (2003) The first "for sure" remake. They change the name of the family for some reason.
• The Texas Chainsaw Massacre: The Beginning (2006) The Prequel to the remake
• Texas Chainsaw 3-D (2013) Claims to be a direct sequel to the original 1974 The Texas Chainsaw Massacre which I guess ignores the original Texas Chainsaw Massacre 2?
• Leatherface: The Texas Chainsaw Massacre Prequel (201X) just announced prequel to the 1974 The Texas Chainsaw Massacre, not to be confused with Letherface: The Texas Chainsaw Massacre III or The Texas Chainsaw Massacre: The Beginning or The Texas Chainsaw Massacre: The Next Generation.

They've recently released a cleaned up version of the film in theatres. I've seen it and although I'm not a fan of the film, it is the best looking and sounding the movie has ever been.