Great multiplayer is what makes Melee what it is; a solid fighter
I personally think that Super Smash Bros. Melee is a little bit over appreciated, but that does not mean it is not a great game. Sure it has great multiplayer with friends and family, but say you don't have anyone to play with, the CPUs really aren't that fun to play against; nor do they pose much of a challenge, and this can become very boring after a while.
There is virtually no story to Melee, but there is still single player modes; but they don't bring much to the table. For single player modes there is classic and adventure modes- there is not much to say about them because they are quite shallow in size and creativity.
The gameplay is fairly well done, but it could have used some work; the controls feel kind of stiff from time to time. Melee has, of course, great characters; from Mario to Link to Samus, they are pretty much all here. In the end Melee has very well done multiplayer, but the single player leaves much to be desired and could have been done so much better.