Jumpman is a platform game written by Randy Glover and released by Epyx in 1983. Originally developed for the Atari 400/800, versions were also released for the Commodore 64, Apple II, and IBM PC.
The object of the game is to defuse all bombs in a platform-filled screen. Jumpman defuses a bomb by touching it. According to the story, these are placed on Jupiter by terrorists. Jumpman can climb up and down ladders, and of course jump, and there are two kinds of rope each allowing a single direction of climbing only. Hazards include falling, "smart darts" (small bullets that fly slowly across the screen, but when orthogonally lined up with Jumpman, greatly speed up and shoot straight in his direction) and other hazards that are unique to a certain level.
Points are awarded for each bomb defused, with bonus points available for completing a level quickly. Jumpman's game run-speed can be chosen by the player, with faster speeds being riskier but providing greater opportunity to earn bonus points.
"Jumpman" was also the original name used for Mario in the 1981 arcade game Donkey Kong, which featured several elements (such as the ladders and levels aspects) that would appear in Jumpman. Randy Glover has stated that Donkey Kong was the original inspiration for Jumpman, although it is not clear that the naming commonality is anything but a coincidence.
Source: Wikipedia, "Jumpman," available under the CC-BY-SA License.