I'll start by saying this right away; The most fun I've ever had with a single game is with Super Smash Bros. Melee. Sure, it doesn't have the best graphics you'll ever see in your life. They're decent, but nothing spectacular. But the core gameplay, especially if you have friends around, is outstanding.
If you aren't familiar with the Super Smash Bros. series, it is almost a genre by itself. If isn't like other fighting games; there's no health bar. Instead, each character has a percentage on the bottom of the screen that shows how much damage he or she has taken. This can get up to 999%, although it doesn't get over 200% too often. So how do you die? Well, you literally have to get blown off of the screen from someone's attack. As the percentage of damage taken gets higher, the higher and farther you will fly into the air. Once it gets near 100%, any attack can potentially knock you off the stage. This makes the game completely unpredictable. Your character could be getting the crap beat out of it, but if a valuable item drops, the tide of the battle could change. There is a very large amount of different items that can drop, as well. These range from Hammers(like the ones in original Donkey Kong), PokeBalls(which summons a random pokemon, and there are probably about 50 different pokemon that can potentially come out), Light-saber-esque weapons, and Laser Guns, among many, many more.
If you played the SSB game on N64, you'll be pleased(or not, maybe) to know that combat hasn't really been changed. Super Smash Bros. Melee is still a primarily offensive game, and the fighting system isn't really deep at all. In my opinion, this is a great thing -- it adds to the "pick up and play" feel of the game, which in turn adds to the glamour of the multiplayer mode. Any of your friends, whether they play video games or not, can pick this up and give you a challenge. Hell, I even had my 6-year-old brother beating up computer opponents. Anybody can play it with ease. And if you have 63 spare friends doing nothing, you can even setup a 64-man tournament, which would probably take all day, but would be a helluva time.
There are many classic(and not-so-classic) Nintendo characters included in the game. These range from obvious choices such as Link, Mario, and Samus to choices that not many people would expect, such as the Ice Climbers, Fire Emblem characters Roy & Marth, and Mr. Game&Watch(in all his 2D glory). Any hardcore nintendo fan will love the different characters they can choose from.
Another neat new feature in SSBM are the trophies you can collect. There are literally hundreds of different trophies you can get from just finding them or buying them with coins. There is a trophy that represents almost every Nintendo first-party series to date, including titles like Custom Robo 2 and Mach Rider. Honestly, who expected anything from Mach Rider and Custom Robo 2? There's even a trophy from Duck Hunt, for all the Duck Hunt fans out there. Even some of the biggest Nintendo fans could say, "I never knew that!"
I have only touched on some of the great aspects of the game...there are still many more. This game sells Gamecubes. If you have a Gamecube and DON'T have this game, get it. You'll be doing yourself a favor.