Kirby's Adventure, released for the NES in 1993 (2 years after the SNES was released!), is the second Kirby game in the series. However, it was the first Kirby game to establish his signature power to eat enemies and copy their special powers -- a feature which would be present in every Kirby game following.
Story: One day, Kirby wakes up from a nap and realizes that he didn't have any dreams. He goes to the Fountain of Dreams -- the source of all dreams in Dream Land -- and discovers that the evil King Dedede has stolen the Star Rod and broken it into many pieces to be distributed to his strongest minions. Without the Star Rod, the Fountain of Dreams cannot function. It is up to Kirby to defeat Dedede and his minions and restore the Star Rod to its rightful place.
Gameplay: Kirby's Adventure is a standard platformer in most respects. However, it has two unique features: the aforementioned copy ability and flying. Kirby can inhale any minor enemy and use their abilities, if they have any. Kirby can also fly indefinitely (this ability is limited in later games -- Kirby 64 being the first one). The game is divided into seven major areas. The overworlds contain doors to numbered sub-levels, as well as minigames and several other features.
Level 1: Vegetable Valley
Level 2: Ice Cream Island
Level 3: Butter Building
Level 4: Grape Garden
Level 5: Yogurt Yard
Level 6: Orange Ocean
Level 7: Rainbow Resort
Captain Aardvark also provided this wonderful(ly horrifying) clip of Kirby. Watch it and be spooked: http://www.youtube.com/watch?v=0IOMkI9mmhs