You should never BASE Jump. It is one of the most genuinely dangerous sports on the planet. But with that out of the way, you should definitely learn all about this pastime where people jump from tall structures and outcroppings for fun and thrills.
Leaping from Half Dome or anywhere else in Yosemite has been illegal since but the sport of BASE jumping from the Valley's cliffs is soaring in popularity. Many jumpers call El Cap the birthplace of the sport.