Bicycle theft is extremely common near campus and in Berkeley in general. Secure your bicycle with a U-lock at all times – secure the front wheel, the rear wheel, and the frame whenever possible. It's easiest to do this by using both a U-lock and a cable, with the U-lock securing your front wheel and frame and the cable looping through the rear wheel. If your bike has quick-releases, consider replacing them with screws, especially if you have a quick-release on your seatpost. (A quick-release is the little lever which makes it possible to remove a wheel or a seat without a screwdriver or hex key.)
If you have to lock your bike to a sign or a fencepost, check that it is securely attached to the ground. If your bicycle is really nice, consider buying a cheap one for everyday use. People will still try to steal it! Erik Petigura bought a used bike for $20 and had it stolen after two weeks because he was using a cable lock. Register your bicycle with police to (slightly) increase your chances of recovery if it is stolen.
Berkeley is full of inattentive drivers, and the chaos of cars/bikes/pedestrians near campus is challenging even for skilled drivers. Bike carefully, and make eye contact with drivers whenever possible! City-designated bicycle boulevards (denoted by purple signs) generally have less automobile traffic than other streets. But even on bicycle boulevards, it is unwise to plow through intersections at full speed. Wear a helmet. On campus, be extra careful of pedestrians – many students wear headphones and walk with their heads down, completely oblivious to their surroundings.
If you're not used to biking in wet conditions, do so carefully. Metal surfaces, such as manhole covers or the random plates that are all over campus, become extra-slick. In general, anything that's not pavement becomes more dangerous – even the paint on the road provides noticeably less traction when wet.
UCPD is looking for opportunities to ticket you!! Last year (2010) I was fined $230 for riding in a dismount zone. Last week (2011), I saw a cyclist get pulled over and ticketed for rolling through a stop sign near Memorial Glade. When riding on campus, obey the letter of the law. In particular, dismount and walk your bike through Sproul Plaza and the areas near Dwinelle and Wheeler halls.