Video games have gone through dramatic change since their inception with Pong and other very early titles. Games have gone through such transformations as simple left to right object movement, top to bottom object movement, platform jumping, 3-D action and games where you are in complete control of the characters with your bodily motions. One of the early shifts occurred between side-scrolling/top to bottom games evolving into those with platform jumping.
Simply put, platform games involve making your character jump from one platform in a game to another platform. There were many games featuring this in the 1980s and some of the more popular games were: Super Mario Brothers, Castlevania, The Legend of Zelda: Adventure of Link, Metroid and Donkey Kong. Each of these games involved different types of platforms in different sizes and shapes.
The simplest platform game of those listed above was certainly Donkey Kong. This game was challenging for other reasons however the platform jumping in it was the easiest, mainly due to the fact that there was not as much danger of falling off and dying as there was in other games. An argument could be made that objects being thrown at you while jumping makes this challenging, however that is common in the other games but without the danger of falling to death.
For example, in The Legend of Zelda: Adventure of Link, there are many scenes where you must jump over water (or air) onto another landing area while monsters are flying at you in the air. In addition to making sure you land on the next platform, you either had to kill the enemy flying at you or time your jump so that you would avoid it. As if that were not enough, some enemies would shoot objects at you from mid-air; if any of these objects hit you while you were jumping, it would likely push you backward and off the platform, into your demise.
Castlevania introduced another variable to the platform jumping with items you had to latch onto in order to make the next platform. The main characters in the early Castlevania games fought with a whip, and in some areas of the game that whip was needed to latch onto an object suspended in mid-air in between two platforms. It was your job to latch on and swing your character to the next platform while, as you can probably guess, avoiding an enemy looking to knock you out of mid-air.
Metroid had a top to bottom platform jumping challenge, where you would not necessarily die from falling but it could set you back quite a bit in the game. For instance, there are some areas of the game where you need to climb 10-20 or so platforms to reach a door; at any point an enemy could hit you in mid-air and cause you to fall past all of the platforms you just jumped on.
The strategy for all platform games is patience and timing. Before you begin jumping from platform to platform, get a feel for any enemies that will hit you mid-flight and whether the platforms moved or dropped out from underneath you (this is common in Super Mario Brothers). Simply rushing from one platform to the next will cause you to lose lives more often than not, so be patient and learn the challenges ahead!