People play sports. People watch sports. It's a fun aspect of life for those who aren't interested in talking to one another in a way that involves their lives.
Collegiate sports are the official sports teams that represent UC Berkeley in the PAC 10. Of course the official collegiate level of Cal sports comes under the banner of Cal Athletics, aka the California Golden Bears. Though the strength of collegiate teams vary from sport to sport and from year to year, Cal generally has a well respected athletics program. Tickets for sporting events can be purchased online or through the Ticket Office, make sure you get student tickets (assuming you are a student).
Here's a list of the official sports for men and women.
|Mens Sports||Women's Sports|
Intramural sports are organized and run by the Recreational Sports Facility (RSF), which allows students and RSF members to build their own intramural groups and compete in various team sports. Intramural teams are a step below collegiate athletics, but above the level of a pickup game. Intramural sports offer a structured competitive environment for your average student.
Here's a list of some intramural sports:
Club sports offer students competition, instruction, and recreation in 27 sports and activities. The program serves as a competitive alternative to intramural sports, physical education, and intercollegiate athletics by offering team members professional coaching, league travel, and participation in national tournaments. Currently, over 1,800 members of the campus community participate in the program. 
Here's a list of the club sports:
Recreational sports basically covers anything you can organize on your own. The RSF is equipped to handle many different sports, and you are welcome to play a pickup game of basketball with your friends or play a game of racquetball with your roommate. The easiest way to get involved in a sporting group is to look around your dorm area and find out who enjoys playing sports. Lots of groups will just set up shop and create their own pickup teams and use the various facilities around campus to exercise. Usually they're based from the same dorm, a social group, a fraternity/sorority, or any kind of arrangement that brings people together.