Star Trek: 25th Anniversary is a 1992 adventure video game developed by Interplay and published by Ultra Games for the Nintendo Entertainment System and later a different version was made with the same name (not a port) on the Game Boy.
It begins as the USS Enterprise is approaching the planet Sigma Iotia II. The ship is confronted with a tear in space-time that sends them to an unknown area of space. While attempting to escape, the dilithium crystals, needed to travel at warp speed, have been fused and are useless. The Enterprise is trapped in a decaying orbit above an unknown planet, but Spock detects small amounts of dilithium crystals on the planet. Once the crystals are found, the Enterprise still needs to get back to Federation space, (stopping for better crystals to continue the journey), figure out what caused the tear in space-time, and find a way to fix it.
When an away team beams down to a level, the gameplay becomes graphic adventure game styled. Most of the time, progress in the game requires the player to interact with various life forms on a world, find objects, and solve puzzles. While each character is equipped with a phaser, violence rarely is the ideal solution to any puzzle.
Source: Wikipedia, "Star Trek: 25th Anniversary (NES video game)", available under the CC-BY-SA License.