Possibly the oldest example is Bubble Bobble, which had three different endings — the BAD END obtained by beating the final boss Super Drunk with only one player alive (this boots you back 25 levels on Normal and 50 levels (HALFWAY!) on Super Mode), the Good End obtained by beating the boss with two players alive, and the Happy End obtained by beating the boss with two players alive in Super Mode — which has to be enabled before starting the game with a code you get from the Good End. This was taken literally in a sequel, Bubble Symphony, where the players can go to multiple worlds and see a bad ending exclusive to that world if they don't get the stuff they need. With successive games though, the idea of requiring two players sticking together to the end has been dropped, but in two sequels, there is a Super Mode to play.
In pretty much any Sonic the Hedgehog game where collecting the ChaosEmeralds is optional, if you beat the game without collecting all the Emeralds, then you're treated to a post-credits scene with Robotnik in possession of the Emeralds, laughing to himself. Beating the game with all the Emeralds gives a more cheerful scene.
A nasty example of this is Sonic the Hedgehog 2 (8-bit version). If Sonic does not collect all of the Chaos Emeralds, than Eggman/Robotnik escapes, and the ending implies that Tails was killed.
Shadow the Hedgehog has ten different endings (some of them more different than others) and a helpful in-game diagram that shows how to reach them. (The one you get depends on how many “Hero”, “Dark”, and “Normal” missions you complete in the flowchart-like structure of the plot.) Finding all ten of them unlocks the now-traditional "Last Story", an extra level and the Perfect Run Final Boss that lead to an eleventh ending. While the Last Story area takes place in the area of the "hero" endings, after you've collected all the Chaos Emeralds, none of them quite match up with the situation at the beginning of the Last Story.
In Contra: Hard Corps for the Sega Genesis, there are four different paths, each with its own ending. The player must choose between two branching paths at the end of the first stage. The two paths converge to a set of common stages until the player is forced to choose between another pair of branching paths during the fifth stage. The path the player took earlier, along with the path he takes afterward, will determine the final set of stages. There's also a fifth ending if the player completes the secret coliseum stage, as well as a sixth ending in which the player joins Colonel Bahamut's army (although the game counts this as a Non-Standard Game Over).
Both Contra: Shattered Soldier and Neo Contra have a Bad Ending where the enemy base is destroyed with the heroes still inside, as well as a segmented Good Ending in which the full version can only be seen by maintaining an S rank throughout the game and defeating the True Final Boss.
Contra 4 has a different ending for each difficulty setting. Easy mode only takes you to Stage 7, giving you an Easy-Mode Mockery. The ending on Hard shows a different artwork, along with a different ending message, than if you beat it on Normal.
Donkey Kong 64 has a Segmented Ending in that, if you collect less than 100%, you just get the credits with a bit of aftermath behind it. If you collect 100%, you get to watch the credits, and K. Lumsy swimming with the Kongs on his stomach and chest. If you get 101%, however, you get the credits, K. Lumsy's swim, and fake Hilarious Outtakes.
The PC game Mechwarrior 4: Vengeance had two possible endings. There were two second to last missions. In one, you make a raid on an enemy storehouse. The second option is to launch an assault to save the player character's sister from an enemy attack. The first option will result in having the most powerful mech in the game for the most difficult mission, but will result in one of your better NPC pilots going rogue to attempt to save the sister. After completing that mission, your trusted mechanic adviser chews you out for leaving your sister to die and leaves your employ. This results in a final cutscene in which the sister, mechanic, and rogue pilot are all absent. In this ending, you become a hardened and almost despondent Duke. The second mission will result in your character not having access to the most powerful machine, but it is the "good" ending where you have kept all of your pilots and allies. In this ending, your sister becomes Duchess, and you decide to go become a mercenary lance, which suits your temperament better. Both endings result in you winning the game, leaving it up to player preference.
Interestingly, the expansion, Black Knight, assumes the "Bad" ending happened, as you play as a member of a mercenary outfit hired to kill the very character you played in MechWarrior 4, who has become a tyrant.
The other expansion, Mercenaries, had three endings. If you sided with the pro-Victor faction, you became the guard unit for the new Lyran Archon. If you threw in with the (eventually defeated) pro-Katherine faction, you could go rogue and become a leading player in the Chaos Marsh. Alternatively, you could join Clan Wolf by fighting a Trial of Position and go on to rescue Katherine.
Mega Man X4 had two different endings depending on which player character was used. Both X5 and X6 had three different endings that depended on chance. Whether Zero turns Maverick or not, which also dictates if you can still play as him, is random, though completing various objectives tips the odds in your favor.
Then there's Rockman 4 Minus Infinity, which has a variation - the ending's basically the same, but there are a lot of minor differences.
If you rescue Rush during the final level, Mega Man will use Rush Cannon on Wily's space ship upon escaping the castle. Otherwise, Mega Man will collide with the space ship with Hell Wheel instead, destroying it regardless.
Eddie, Rush, and Beat make appearances depending on if you used the Recycle Inhaler on the former and/or rescued the other two during the final level.
If you turned Toad Man into a toad during the rematch and spared him, he will appear in the first part of the credits, hopping alongside the train.
Depending on what happened to Rush, Eddie, and Beat at the end of the game, they will appear either in color or grey (ala Mega Man X2) in the "Presented by Capcom" screen.
In Splatterhouse 3, there are four endings, three bad ones and one happy one. If you fail to save your wife or son (or both, the worst-case scenario) during the game, you get one of the bad endings. If both survive, you get the happy ending.
The Famicom version of Karnov has three endings, all of which are "good."
In Luigi's Mansion, after you complete the game, Professor E. Gadd builds Luigi a new house, and how nice a house he builds depends on how much treasure you've accumulated during the game. (Curiously, getting the worst house is actually harder than getting the best one. You'd literally have to pick up no treasure except the stuff you automatically get. Some players have actually tried to finish the game with the worst house as a challenge.)
Wario Land II has several different gameplay paths that branch out and intersect, and several different endings to go with them. Most of the endings come down to a variation of the same thing, though.
Its predecessor also has multiple endings, depending on how many coins and treasures were collected at the end of the game.
In Wario World, the way the Spritelings restore Wario's castle at the end depends on how many the player rescued. You could either receive a tent, a wooden fortress, an empty stone castle, a slightly less empty turquoise castle, a gold castle, or another gold castle filled with riches.
In Wario Land 4, there were multiple endings depending on the difficulty level and amount of treasure chests collected from boss battles. You'd first have the appearance of the princess rescued change (ranging from a female Wario clone to a child to different forms of princess), then the car Wario's driving would look different based on difficulty level (normal was the Wario car, hard a truck, and super hard a hover car), the pictures show in the Credits Montage would change based on treasure collected, the music would change based on difficulty level and treasure collected, and you'd get some extra pictures showing Wario on a date if you beat it on super hard and got 100% completion.
In Kid Kool and the Quest for the Seven Wonder Herbs, the player has a total of three days (each day represented by one hour real time) to collect seven magic herbs to save the dying king from his terminal illness. The quicker the game is completed, the better the ending:
The best ending, which is attained by finishing before the timer hits one and a half hours: The King lives, and will hand over the throne to Kid Kool in the future in addition to the Standard Hero Reward.
If the game is finished between two and two and a half hours, the King lives and Kid Kool is rewarded with a box of jewels.
If the game is finished between two and a half and three hours, the King lives and Kid Kool is rewarded with money.
If the game is finished after three hours, it gives the bad ending: the King dies and Kid Kool gets nothing.
In the Sega Genesis version of Beavis And Butthead, the normal ending has the two attending a concert featuring the band GWAR. However, if you've collected the cat, the scissors, and strips of leather, you go backstage and Beavis and Butt-Head get to perform in the concert!
The normal ending being the destruction of the enemy HQ in Saint Ark. The other two are only available if the ZOE ace pilot is shot down during said mission.
The bad ending has a cruise missile launched from a nearby submarine, which destroys the city if not shot down.
The best ending has the allied forces attack the enemy's second HQ, a fortress with a larger cruise missile ready for launch.
The uncut Ace Combat 3: Electrosphere is so far the only Ace Combat game with multiple endings: one for each major faction (UPEO, General Resource, Neucom, and Ouroboros) and one lone-wolf ending (technically, also Ouroboros).
Kirby 64: The Crystal Shards is notorious for 3 things: collecting items (the eponymous Shards and Enemy Info cards), three 4-player mini-games, and of course, cutscenes. The game has 2 endings that are unlocked depending on if you've collected all of the Shards or not. If you're 99% or under, Kirby and friends leave Ripple Star after defeating Miracle Matter and the final shot you see is a sinister look on the Queen's face. If you've collected all of the Shards, the restored crystal blasts the fairy queen with a light beam, expunging a cloud of Dark Matter from her that flies into space and creates the final world, Dark Star. Kirby and Ribbon must then fight 02(which is quite difficult, since he is the True Final Boss). The real ending has Kirby and the others rewarded with crystal medals after defeating 02, and Ribbon kisses the little puffball, who proceeds to blush and trip down the stairs in a comical manner. Note that if you get all the Shards on your first try, the bad ending isn't Lost Forever in the cutscene menu if you didn't actually see it during normal gameplay; completing the game unlocks it in addition to the good one.
Kirby games are fond of this in general, stopping at the boss of the last area and giving a mildly cryptic ending unless you collected all of their respective plot coupons. Dream Land 2 and 3 both gave the player a rundown of all the enemies in the game before showing a question mark on Dark Matter.
In Gekisou Sentai Carranger: Zenkai! Racer Senshi, if the Rangers get 250 gears, RV Robo will be formed, and the good ending will be obtained (though it's rather perfunctory). Otherwise you get the "BAD END," where after the Final Boss, the Bowzock run wild and cause an Earth-Shattering Kaboom.
The first Crash Bandicoot (1996) game features two endings — and interestingly, it's not actually clear which ending is the better one story-wise. The harder ending requires the player to collect all the gems, after which they can traverse The Great Hall and escape the islands with Tawna, followed by a humorous "Where Are They Now?" Epilogue. The other ending involves the player actually defeating Cortex.
Donkey Kong Country Returns had three endings. If Donkey Kong and Diddy Kong are present, Donkey Kong and Diddy will fall towards the moon before Donkey Kong pounds it, ending the Tiki tribe. Diddy then makes a safe landing. If only Donkey Kong is present, the same thing happens, this time without Diddy. Donkey Kong will keep falling unti Diddy saves Donkey Kong. If only Diddy is present, Diddy will fall towards the moon and tries to use his jetpack, but the jetpack goes out of control, causing Diddy to land headfirst into the moon, which ends the Tiki tribe. Donkey Kong then catches Diddy as he falls.
In Mighty Bomb Jack, beating the final stage always involves rescuing King Pamera. With one crystal ball, the Queen can also be rescued, and with two crystal balls, you Save the Princess too. Getting to the true final room and best ending requires all of the above and five secret coins.
The Pokémon Peace Squad games fall under this due to there being Loads and Loads of Characters to play as, all of which are included in cutscenes. You can defeat the Big Bad and save the world with Ash Ketchum, a League Champion like Lance or Cynthia, or even one of various one-shot characters from the anime. For example, you can have Sonrisa, a one-shot Sunflora gardener, defeat a One-Winged Angel Ghetsis fused with a god-like Pokémon and restore the multiverse! The possibilities are nearly endless!
On top of all that, Pokémon Peace Squad 2 included two endings after clearing Draco Starbase, one for Normal mode and one for Expert Mode. For the Normal one, you simply escape the Rayquaza Jet in an Altaria Orbiter with the Chaos Meteors and Prof. Oak talks to you about Meta Leader and who he might be. For the Expert one, the Altaria Orbiter has damaged landing-gear and you end up having to make a splashdown in the Lake of Rage in a very awesome sequence.