1. Catherine was crushed to death by a horse whilst attempting to have sex with it (usually the collapse of a harness/lifting mechanism is blamed).
2. Catherine died on the toilet.
The Truth (1):
Catherine died in bed of illness; there were no equines involved and a Catherine/horse nexus was never attempted.
How Did This Myth Start?:
Catherine the Great of Russia's death while attempting an unusual practice with a horse is one of the most virulent myths in modern history, transmitted by whispers in school playgrounds across the western world. It's unfortunate that one of history's most powerful and interesting women is known to most people as a beastite, but the combination of perverse rudeness and the relative foreignness of its subject makes this a perfect slander.
So if Catherine didn't die while attempting sex with a horse (and just to reiterate, she absolutely, 100% didn't), how did the myth arise? During past centuries the easiest way for people to offend and verbally attack their female enemies was sex. Marie Antoinette, the hated queen of France, was subjected to printed myths so deviant and obscene they would make spam emailers blush and certainly can't be reproduced here. Catherine the Great was always going to attract rumours about her sex life, but her sexual appetite – while modest by modern standards - meant that the rumours had to be even wilder. Historians believe the horse myth originated in France, among the French upper classes, soon after Catherine's death as a way to mar her legend.
The Toilet Myth:
However, in recent years another myth has emerged. Take a quick look around the web and you'll find pages debunking the idea of Catherine with the horse while stating that the great Empress of Russia really died while on the toilet. Admittedly such sites are quick to point out another myth, that Catherine’s bloated body was so heavy it cracked the toilet (this variation was also spread by Catherine's contemporary enemies), but the toilet features prominently nonetheless. Indeed, some sources quote thus from John Alexander's marvelous biography of Catherine:
"Sometime after nine chamberlain Zakhar Zotov, not having been summoned as anticipated, peeked in her bedroom and found nobody. In a closet adjacent he discovered the Empress on the floor. With two comrades Zotov tried to help her up, but she barely opened her eyes once before emitting a faint groan as she exhaled and lapsed into unconscious from which she never recovered." (Page 324, Catherine the Great by John T. Alexander, Oxford, 1989)
If you take 'closet' to mean water closet, another name for toilet, the quote seems fairly conclusive. Unfortunately, this 'fact' isn't true but the product of a desire for belittling humour: the toilet is a common enough location of death to be true, but still intrinsically humiliating, especially for a great empress.
The Truth (2):
Catherine may have never recovered full consciousness after her collapse, but she wasn't yet dead. Alexander's book goes on to explain (in paragraphs rarely quoted) how Catherine was laid in her bed as doctors tried to save her body and priests made rites to save her soul. Throughout she was racked with pain, her convulsing appearance causing great distress to her consorts. It was over twelve hours after Zotov found her, well past nine o'clock at night, that Catherine finally died of natural causes, in bed and surrounded by friends and carers.