There are 12 playable characters in Super Smash Brothers; eight that are available at the start, and four that can be unlocked in single player mode through completion of certain challenges. They all have certain advantages and disadvantages, and although this game is very well balanced, certain characters are better than others are. However, Super Smash Brothers 64 character tiers are very subjective, so characters will not be listed in order from best to worst. I give a basic summary of characters, and go can go to the in-depth guides for more specific info, but you will have to figure out character rankings for yourself.
Captain Falcon
Probably one of the most dominating players in the game, Captain Falcon's greatest assets are his speed, his backwards throw, and his fire kick. His Falcon Punch, while powerful and certainly effective in certain situations (notably, immediately after being given a new life and while still invincible for a couple of seconds), should not be relied upon too heavily because it requires about two seconds to charge up during which time Falcon is vulnerable to any number of attacks from opponents. The Falcon Kick useful move (note that it is not nearly as powerful as the Falcon Punch) because with it you can attack a player from a distance (i.e., the move glides Falcon across the board). The Falcon Kick is particularly effective if used when an opponent is already off the board (i.e., Do a Falcon Kick off the edge, hit the opponent, and jump back - Falcon can make it). The Fire Kick (Falcon's Forward + A) is also a devastating weapon, but, again, be prudent when using it because it is a slightly slower move than, say, Link's Forward + A move. The Fire Kick should be used primarily to finish players off once they are off the edge and jumping back. Finally, Falcon's throw, particularly his reverse throw (R + Joystick away from the opponent) is probably his most useful attribute. For one, players are defenseless against the grab (a shield does not block it). Moreover, it can be used to clear out a brawl. Falcon's greatest strengths, unlike Link's, do not lend themselves to melees, so it is generally in Falcon's best interest to throw players away from one another and then isolate. Falcon's speed enables him to run quickly up to players, grab them, and then throw them before they can defend themselves. When near an edge, using the reverse throw to launch players off the board is an effective strategy, too.
Donkey Kong
The large primate from the old arcade-style Mario games is back again. This time he's larger and better than ever. He is the hardest character to K.O., because of his size. Some can go on until 300% damage using him. Donkey Kong is a mix of endurance and power. He has rather mediocre speed, but his power makes up for the loss. His main B button attack, the Giant Punch takes around 3-4 seconds to charge (In mid-air or on the ground) just don't let him get hit, or he'll have to start over again. His (Up+B) attack, the Spinning Kong is used for getting back up on the stage after your two jumps. The Spinning Kong is a horizontal move, meaning it will get you little or no air. This move lets Donkey Kong imitate a helicopter and literally spin for a short amount of time. Finally, his Hand Slap/Ground Pound is by Down+B. This little move is a killer when you use it in the Mushroom Kingdom (Classic Mario World) level (In the Bottom Left Area, where there's a ceiling), or Hyrule Castle's little greenish building on the right side of the stadium. This move will get all enemy characters that are standing on the ground into the air. Because of the two spots in the two levels that I have mentioned above, the Hand Slap move will cause opponents to go up, hit the ceiling and fall down again... *Repeat Many Times... *Cough *Cough.... Also, the Z+A (throwing move) will let you pick up an opponent and simply toss them. You can also walk with them on your back. (Try jumping off the stage with your enemies on your back) A special little thing about Donkey Kong is his ability to move with crates or barrels. However, he can only jump once when his is holding these objects.
Fox
Fox McCloud is the protagonist in Nintendo's futuristic Starfox fighter-plane games. Although you never saw his character in action (only his ship), his special moves in Super Smash Brothers are gracefully taken from his ship's maneuvers. He is a fast, somewhat light character with some powerful moves.
Jigglypuff
Kirby
Hailing from the old-school Kirby series of the original NES days, Kirby carries into the game a variety of abilities he has in the other games in his series, including the ability to suck other characters inside himself and take their abilities. While some of his moves are regarded as cheap by many players, when mastered, his drill kick and Final Cutter attacks can be lethal.
Link
His speed is slow, and he has the worst jumps in the game but he is very powerful. Pressing Up+B while in the air causes him to spin his sword around, making him go higher. Link has a good arsenal of weapons. He is able to throw a boomerang, and bombs. But bombs are on a timer, so don't be cought holding them when they explode, as the blast radius also damages you.
Luigi
Mario
When one thinks "Nintendo", this guy comes to mind. A plumber with a moustache and a penchant for jumping who happens to be in love with a perpetually kidnapped princess (I mean, what the heck, Nintendo?), he and his games fill many of the spots for top-selling games of all time. In Super Smash Brothers 64, this red-capped and blue-overall wearing Italian is a good all-around character. He has fantastic aerial recovery time, a great u-air juggle, and very annoying fireballs, but isn't quick enough to keep up with the likes of Fox or Captain Falcon.
Ness
Ness is a young psychic boy (exact age unknown), protagonist from Nintendo's Earthbound RPG series. Ness is a hidden character, so you will have to unlock to use him in versus play. To do this, you have to beat the game on Normal difficulty with 3 stock, no continues, and then defeat him in 1v1 combat. He is probably one of the more difficult characters to play with, since his third jump is very tricky to pull off for a new player, and his floaty, circular second jump can weird out even veteran players. He is a fairly light, slow character with powerful attacks, and is the only character with a healing move.
Pikachu
An electric Pokémon from the game series of the same name, Pikachu is very powerful and agile. He is so powerful and agile, in fact, that he has been considered "cheap" by the unenlightened. I myself find few disadvantages to the little guy, but then again, he's my main. He has one of the best recoveries, if not the best, in the game and has a simply unavoidable edgeguard. He suffers from short range on the ground, is relatively light, and takes a good level of skill to play well, but this electric rat could very well be your route to victory.
Samus
Samus is a master of distance, but an all around good character to play. Various moves need to be mastered to be an effective Samus player.
Yoshi
Yoshi comes from the popular Mario Brothers and Yoshi series, and brings into the game some of his abilities from the series such as his ability to suck people up with his long tongue. He is generally considered one of the worst players in the game due to his lack of a third recovery technique (which he attempts to make up for with an extra-high second jump) and his general slowness. He does have powerful melee attacks, though their slowness makes them easily avoidable.