Snake, Nibbler, Tron

This is rather complicated. For one thing, Snake, Nibbler, and Tron are three different concepts, but their history is so interwoven that they cannot be regarded seperately. And exact information is often difficult to obtain for the earlier implementations.

Blockade, Gremlin, 1976: This is the arcade machine that started it all. Gameplay is what later would be known as Tron, two players draw lines on the screen and try to make the adversary crash. Blockade was strictly two-player, no AI was provided to play against. Still in the same year, Gremlin released another game called Comotion which seems to have differed from Blockade only in small details. In January 1977, Atari released a machine called Dominos which was more or less the same as well.
Hustle, Gremlin, 1977: This machine is already a lot closer to the Snake concept as it is known now. It introduced targets the players try to hit, never more than two targets on the screen at the same time. The targets have values, which can be negative as well and are not always displayed in advance. The snakes have now a tail of finite length, which increases not by hitting targets, but through crashes.
Surround, Atari 2600, 1977: While based on Blockade, this game featured 14 different game modes, some of which allowed diagonal movement, some for one and some for two players. In the last two modes, it was simply a drawing program.
Worm, Blockade, Hustle, TRS-80, 1978/79: Three games by Peter Trefonas, distributed on tape by the CLOAD magazine. Blockade and Hustle are clearly remakes of the respective Gremlin arcade machines, Worm had somewhat simpler graphics and seems to have introduced a sort of maze.
Hyper-Wurm, F. Seger, TRS-80, 1979: Probably an enhanced remake of Peter Trefonas' Worm. There's a screenshot on Wikipedia, I don't know more about it.
Worm, Michael Toy, 1980 (?): The first ever game written with the help of the curses library. Together with Glenn Wichmann Michael Toy later created Rogue. Worm has been part of BSD Unix possibly since 4BSD, and the code is still readily available. Worm is similar to Hustle, but the length of the worm increases with the targets eaten.
Tron, Bally Midway, 1982: This game was manufactured as a tie-in with the Disney movie of the same name. It's nothing but the old Blockade, which was featured in the movie as the Lightcycle Game. This sort of gameplay, which it probably rescued from oblivion, has since usually been known as Tron.
Nibbler, Rock-Ola, 1982: This machine put the snake into a maze and a lot more targets on screen. Pac-Man may have been of some influence here. The maze must be cleared before the time runs out. The length of the snake increases by eating. Nibbler can be played by one or two players. There is a good anonymous DOS remake.
Nibbles, QBasic, 1990: This was one of the two games included as sample programs with QBasic. It was probably quite similar to Michael Toy's Worm. It may have helped poularize the concept on the PC, it may also have helped to confuse the distinction between Snake and Nibbler.
RattlerRace, Windows, 1991: This game was written by Christopher Lee Fraley (maybe better known for Rodent's Revenge) and distributed as part of the Microsoft Entertainment Pack for Windows 2.
Nibbly '92, C64, 1992: The Austrian demo group Cosmos Design gave the Nibbler concept a new twist in this game. The whole maze is filled with fruit, every single tile, which makes it much more a puzzle than an arcade game. There's a good DOs shareware remake, Nibbly'96.