Bruce Lee was so fast, they actually had to run his films slower so you can see his moves.

Bruce Lee in Enter the Dragon (1973). Image: Lexinatrix [Flickr]1. Bruce Lee's Family Gave Him a Girl's Name: "Little Phoenix"
Bruce's family never called him "Bruce." They preferred to call him by his nickname "Sai Fon" or "Little Phoenix." It was a girl's name, deliberately chosen by his parents because they believed that evil spirits did not like boys in the family (their firstborn was a son who died in infancy). So, by giving Bruce a girl's name, they believed they could fool the demons into sparing his life!
Actually, "Bruce" was a name given by a nurse at the Jackson Street Hospital, San Francisco, where he was born (Bruce's father was traveling with an acting troupe at the time). The nurse thought that giving the baby an English name would help avoid any confusion with his American birth certificate (yes, Bruce was an American by birth - he never had any other citizenship).
2. Bruce Lee was Part German
Bruce wasn't pure Chinese - he was actually part German (his grandfather from his mother's side was half German).
3. Bruce Lee Never Lost a Fight
Well, actually he lost a fight only once in his life: when he was 13 years old. This loss actually prompted Bruce to learn martial arts from a Wing Chun master named Yip Man. After other students learned that Bruce wasn't pure Chinese, they refused to let him train in their class. Yip Man had to train him privately. (Image: Portland Kung Fu Club)
4. Bruce Lee was a Bad Student
Academics didn't interest Bruce in the least. After primary school, Bruce entered La Salle College, an English-speaking boys' secondary school in Kowloon, Hong Kong, where he often got into trouble. Bruce was expelled from La Salle for disruptive behavior.
Even after his parents moved him to a different school, Bruce kept on getting into street fights.
5. Bruce Lee was an Excellent Dancer and Boxer
Actually, Bruce studied dancing as hard as he studied martial arts: he was an excellent dancer who, at 18 years of age, won the 1958 Hong Kong Cha Cha Championship! Bruce was also a great boxer: he won the 1958 Boxing Championship - by knockout, of course.
6. Bruce Lee was a Philosophy Major
Bruce wasn't just all muscle and no brain. He attended the University of Washington, where he majored in philosophy with focus on the philosophical principles of martial art techniques. As you might imagine, Bruce supported himself in college by teaching martial arts. Later, Bruce dropped out of college to open his martial arts school.
7. Want to challenge Bruce Lee? Just tap your foot on the ground!
After he got famous, a lot of people thought they could beat Bruce - they would walk up to him, tap their foot on the ground (symbolizing a challenge) and then proceed to attack him! Well... maybe not that literal, but Bruce's popularity certainly attracted a lot nutcase trying to prove they're better than him.
One day, while filming Enter the Dragon, an extra taunted Bruce Lee and challenged him to fight. The whole thing went on like this:

"This kid was good. He was no punk. He was strong and fast, and he was really trying to punch Bruce's brains in. But Bruce just methodically took him apart."
"I mean Bruce kept moving so well, this kid couldn't touch him...Then all of a sudden, Bruce got him and rammed his ass into the wall and swept him, he proceeded to drop his knee into his opponent's chest, locked his arm out straight, and nailed him in the face repeatedly."

Typical of Bruce Lee, after the fight he didn't fire the extra - he actually gave his challenger lesson on how to improve!
8. Bruce Lee was Strong
In 1964, Bruce was invited to a karate championship in Long Beach, California. There he performed his famous "One Inch Punch," where he would deliver a devastating blow from only an inch away, sending his opponent flying back!

[YouTube Link]

Bob Baker of Stockton, whom Bruce hit, said "I told Bruce not to do this type of demonstration again. When he punched me that last time, I had to stay home from work because the pain in my chest was unbearable."
... and Fast!
Most martial art films are sped up to make fighting scenes appear fast, but not Bruce Lee's. His moves were too fast to be captured on the regular 24 frames per second film - so they had to film him at 32 fps, and run the film slower so you can see his moves.
9. Bruce Lee vs. Chuck Norris, who would win?
Here's a clip of Bruce Lee fighting Chuck Norris in Return of the Dragon. You can see how fast Bruce Lee moved ... though it's obvious that Chuck Norris would be immune to the One Inch Punch as his one-inch chest hair would absorb the punch with ease!

[YouTube Link]And the most bizarre Bruce Lee fact is this:

10. Bruce Lee's Corpse Acted in his Final Movie!
Bruce Lee was filming Game of Death when he died unexpectedly. So what did the studio do? Well, they rewrote the script so Bruce's character faked his own death to escape the mafia. Then they took footage from Bruce's actual funeral - including close-ups shots of the open casket showing his embalmed face - and work that into the movie! (More on this at Neatorama's post: The Creepiest Movie Ever Made)

Source: Bruce Lee [wikipedia] | Academy of Jeet Kune Do Fighting Technology: Sijo Bruce Lee | Bruce Lee Foundation: Bruce Lee Bio [PDF]