One theory that intrigues me is the 'Dead Raticate Theory'. It basically claims that:
A ~ In Pokémon RBY, the player battles their rival aboard the S.S. Anne; the rival uses a Raticate.
B ~ The player next meets their rival at the Pokémon Tower in Lavender Town; a place which is effectively a Pokémon cemetery, where dead Pokémon are buried.
C ~ The player's rival, before battling with the player again, gives a short speech about the loss of a Pokémon.
D ~ When the player battles their rival, the rival no longer uses a Raticate.
Conclusion: the theory basically concludes that the player injured their rival's Raticate very badly during the battle aboard the S.S. Anne; injuries which led to its death, which is why the rival went to the Pokémon Tower to lay it to rest, which is why he, of course, does not use it in battle against the player.
It's a slightly morbid idea for some; many Pokémon fans will refuse to believe it. I for one though have long been convinced.
This one intrigues me a lot! I am also convinced that this theory is true, I think the writers wrote a very good plot-line or whatever here.. and this always makes me sad, every single time:
"Mere moments after he became Indigo League champion, he was defeated by you. Although he fulfilled his promise to his fallen Pokémon, it was only for a painfully brief instant. In the end, your rival is scolded by his grandfather while you receive the professor's praise. During the course of the game, you steal your rival's innocence, crush his dreams, and ultimately snatch away the love of his own grandfather. Oh, and by the way, your rival doesn't have any parents. He's an orphan."