Basketball by far.
In a close competitive organized game, it's extremely fast, intense, loud, and nothing has the same sense of urgency/fear/pressure at the end of a game. Winning a tournament in high school, coming back from 5 down in the last 5 minutes to win 116-114 is still the best moment of my life.
In a casual pickup game, it's a game anyone can get into, is fun with people of widely varying skill-sets, great players can showboat to a greater extent than any other sport I've seen (I'd say it's a tie with soccer).
Blocked shots, 3 pointers, dunks are some of the best feelings you can have in sport.
The game is athletic, fast, requires a good mixture of speed/strength/technique/skill/intelligence. It does all this while being largely rather safe: you never feel like you're risking your life playing the game, unlike Rugby/American Football. It's amazing for fitness.
Literally the only thing that sucks about the game is how important height is. If you are not >6'0, then good fucking luck going anywhere remotely competitive. I'm very lucky as a 6'3 point guard, but for a lot of people, the game is almost out of reach at higher levels. You look at amazing players like Nate Robinson who have strength, speed, skill, shooting ability, and hustle, yet he still only makes the bench in the NBA. You can make up for a lack of height to some extent, but somebody that is 5'5 is going to find it nearly impossible to stop someone that's 6'0+.
Runners up: Tennis, Rugby (sans injuries), Soccer, Handball.