In Red, Blue or Yellow, play your game like usual, until you come to the ghost tower where the baby Cubone's dead ghostly mother Marowak is. Fight it starting with...
Ghastly
Level 5 (You must trade another Ghastly or Haunter to Gold, Silver or Crystal and breed it to get a Ghastly egg)
Knowing only Night Shade (Do this by taking the Ghastly or Haunter in G/S/C and teaching it Night Shade, then having the move deleter delete all the moves except that one. Then do the breeding with a ditto, and the Ghastly will only know Night Shade)
Note: You MUST have one open slot for a pokemon.
If you attack with these in order, the Ghastly will go first. However, it won't perform a Night Shade. Instead, the backround will become black with stars and the moon. Then, Ghastly will turn into a purple copy of the Marowak ghost's baby son Cubone. You may have guessed, you may not, but what Ghastly did was it possessed the Cubone and made it possess Ghastly itself. Anyway, a little heart will appear over the mother's head, and it will fade away, along with the backround. If you step backwards and use your itemfinder while facing where you were standing, you will find an object called "Tear of Love." The Cubone will come up to you and join your party.
Then, go to Bill's lab. As you may well remember, there is a cloning machine that he used on Eevee, but you were never able to use.
Go up to the chamber on the left and it will say "Deposit DNA Sample Please." Select the tear from your bag and put it in. You will see a flash of light, and Bill's lab will explode. You find yourself laying on the ground in front of the obliterated lab. However there is a bright orb of light emitting from the center of the demolished site. It is a reborn Marowak mother. The Cubone rushes from your party to it's mother. Then they happily walk off the screen. But it is not over.....
You will notice that the chamber holding the tear was not completely destroyed, but the top was ripped off. Go over to it and press A. A bright beam of light will erupt from it, and you will see a little movie scene. You see that all over Kanto, Team Rocket agents are being fried (literally) by red lasers from the sky. Then you come back and are looking at yourself again. Now, for the final part, go to Lavender Town where you last paused your journey...
You may notice several small piles of black ash laying around. I think you know what they are. Go south to leave town. Then the old guy who watches over the cemetary will tell you that he saw everything, he even followed you to Bill's lab, which would explain why half of his head looks burned. He says that he told Professor Oak everything, and that he wants to see you right away. You now are watching a short movie scene of you on the boat, as it rides the waves towards Pallet Town, with a shining pink ball floating after. You arrive and you get:
-A HUGE reception with balloons, banners, even snapshots people took of Rockets getting fried!
-A Master Ball (so you will eventually have two now) for wiping out Team Rocket entirely
-Photo album (restores health if 'read' to a pokemon in your party) of all the pics of Rockets being zapped
-Your Eighth Gym Badge (even if you haven't gotten the previous ones)
-Giovanni's now empty gym, you get to be the gym leader!
Red:
-A Secret TM that prevents any damage to your pokemon for 5 turns
Blue:
-Scene of you surfing and knocking others over by throwing water balloons
Yellow:
-Most of us know that Yellow is the journey Ash took, right? Well, a certain redhead runs at him and I think you know how it ends.
Finally, the pink orb appears over you again and turns out to be a Mew at level 50! (that's pretty good considering that you are halfway through the game, also remember that the Eighth bage makes all pokemon obey you) Mew will then join your party and fill in the space where Cubone was earlier.
Blue and Yellow Versions: Mew will be at level 60, since in Red you got a TM.
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Sorry if that one was too sad or wierd :D