There are a lot of platform games available for Linux. It is not possible to cover them all at once, so we will go for the top five in our article.
Abe's Amazing Adventure
If you are old enough to remember Montezuma's Revenge (or Panama Joe for the Sinclair users), then it's likely that you will enjoy Abe's Amazing Adventure. The plot of Montezuma's Revenge was to reach the treasure chamber of Montezuma II, an Aztec emperor. The player has to collect gold, keys and use equipment such as torches, swords, etc., to save his life from firepits, snakes, spiders and other obstacles. The player can walk, jump, use conveyor belts, and slide down ropes and chains. Abe is the same pyramid-exploring game with minor differences from Montezuma (there are bears, ghosts, crabs and daemons instead of snakes and spiders). Although you may find the graphics a little bit childish (and you are right, because the developer says that he has written Abe for his son's birthday), you will find yourself immersed in the game in a very short time if you are a platformer-type of gamer (like me).
Abe's Amazing Adventure is available from many popular Linux distribution repositories.
Abuse is both a side-scrolling platform game and a run-and-gun game. The game controls are a little bit unusual for platformers: you control the character's movements with the keyboard and the fire with the mouse. You control Nick Vrenna, who has been unjustly sent to a prison where the scientists perform illegal medical experiments on the inmates. A riot occurs and the experiments go terribly wrong: the inmates are transformed into mutants by the substance called Abuse and Nick is the only one that seems immune. You begin the game here, equipped by a laser gun, trying to stop the spread of the disease. And you are the only one to fight everything.
Abuse is available from many popular Linux distributions repositories.
Pachi el Marciano
Our Martian hero of the game is Pachi, created as a comic by Nicolas Radeff in 2001. Pachi lands in a cemetery, connected to a horrible castle, where he has to collect all the different items for the exit to appear. In all the stages, he has to save himself from various dangers, such as rolling skulls, axes, firepits etc.. As the developers say, the game is heavily inspired from 80's platformers Jet Set Willy and Manic Miner. The game is really immersive and I consider it to be a must-play for all platformer lovers.
Pachi is available from many popular Linux distribution's repositories.
Super Tux is a game largely inspired by Nintendo's Mario Bros, in which you control Tux, the Penguin, over various levels and enemies. Tux was out with his girlfriend Penny having a Picnic in Antarctica. Suddenly there is a flash, Tux falls asleep and a creature appears behind an ice bush. When Tux wakes up he finds that Penny is missing. Where Penny had been, there is a letter which reads “Tux, my arch enemy. I have captured your beautiful Penny and have taken her to my fortress. The path to my fortress is littered with my minions. Give up on the thought of trying to reclaim her, you haven't a chance! -Nolok." Tux begins his journey, to rescue Penny from evil Nolok's castle.
In the game, you control Tux and try to finish each level by saving yourself from the obstacles and in meantime collecting the goodies. You can jump and hit the mushrooms to get rid of them, and use the turtles to get rid of other enemies (Mario fans will remember you jump on the turtle first, then jump again to make it slide until it hits an obstacle, tossing everything in its way) but beware the rotating and jumping heads. The ice flowers make you grow to double-size. To make the most out of the game, don't forget to explore: hidden places offer more and sometimes rare goodies!
Super Tux is available from many popular (almost all) Linux distributions repositories.
I do not know where Xmoto fits as a platformer, because rather than a jump-and-run or run-and-gun, you have to play with the physics. You are a biker and try to pass several levels by controlling your bike across different terrains through a variety of clever challenges. You have to control precisely where to accelerate, where and how to decelerate, how to turn your bike, in what position to land and all the physics that you can think of with the motorcycle (in 2 dimensions, thankfully). The first levels are very easy, like a tutorial, allowing you to grasp the controls, but advancing each level presents more difficulty, which you have to tackle with your own dexterity. Don't think that will be easy though, you will find yourself playing levels again and again, trying to figure out how to land over that piece of land and how to turn your bike over.
XMoto is available from many popular (almost all) Linux distribution's repositories