This page explains in detail the interactions between the Parachute series and the Super Smash Bros. series.
See here for interactions between Super Smash Bros. and the overall "Game & Watch series".
Super Smash Bros. Melee[]
November 21, 2001
Parachute
Super Smash Bros.
Mr. Game & Watch's Neutral aerial attack is based on Parachute, consisting in him opening the parachute, causing damage to nearby enemies.
This is considered an in-universe link because Mr. Game & Watch's parachute is considered the actual item from the original game, and also because his trophy implies that he was the protagonist of various Game & Watch games, so Parachute being represented as one of his moves can be interpreted as retroactively revealing that the skydiver from the original game has always truly been Mr. Game & Watch.
This however is arguable, and one may chose to consider it an out-universe (type 3) link instead.
Super Smash Bros. Brawl[]
January 31, 2008
Parachute
Super Smash Bros.
The Parachute sticker
Mr. Game & Watch's Neutral aerial is replaced by a new one based on Tropical Fish; instead he now opens the parachute automatically when reaching the top of the jump after performing his Up Special, Fire, allowing him to slowly slide down. The parachute can be removed by hitting down or performing an aerial attack.
The parachute remains part of Mr. Game & Watch's Up Special in all his subsequent appearances.
The game also includes a sticker based on Parachute, consisting in the player's character about to catch a skydiver into the boat. It can be used by any character and when equipped grants [Arm] - Attack +8.
Super Smash Bros. Ultimate[]
December 7, 2018
Parachute
Super Smash Bros.
Mr. Game & Watch still uses his parachute when performing the Up Special; while most of his moves were redesigned to have him transform completely, this move remained unchanged, likely because of Mr. Game & Watch's default appearance already looking very much like the skydiver.
The Parachute spirit
The game also features a Parachute Spirit, represented by the player's character about to catch a skydiver into the boat, like the sticker from Brawl, but there now also is a shark fin below the boat. This is spirit #697, and it's a Support spirit in the Advanced category (★★). It takes one slot and grants Air Defense ↑ when equipped. It's unlocked by buying it for 1000SP from Sheldon's Place, a shop specializing in weapon-based spirits.
This is considered an in-universe link because the game's plot indicates that all spirits are characters that lost their body in Galeem's attack.
License[]
Copyrights for both series are held by Nintendo.