There are several shuttles that serve the UCSD campus. While technically you need to have your student ID to ride the shuttles, they often do not check. More detailed info (including schedule and maps) can be found here.
Be aware that most shuttle only operate during the academic year so you will need to find alternate transportation during the Summer.
Old City Shuttle
The old City Shuttle route used to go between Mandeville Auditorium and the UTC_Mall. It was replaced in 2006 with two new routes, the Ariba and Nobel routes.
Ariba and Nobel Routes
The Ariba and Nobel shuttles depart every 10 minutes from the Mandeville Auditorium. The Ariba shuttle passes by the Vons on Regents/Ariba and stops at LaJollaDelSol. The Nobel shuttle travels past LaJollaVillageSquare. They don't ask for it every time but you should have your student ID available to ride on the shuttle.
It does get quite full in the mornings (between 8am and 11am) coming to campus (particularly in the half hour before classes start). Depending on where you are in the shuttle route, using this to get to campus may not be a viable way to get to campus in the mornings. An alternative is to use Route48.
Mesa Shuttle
This shuttle runs between campus and the MesaApartments. It is one of the shuttles that runs year round. Its on-campus stop is by the StudentServicesCenter.
Coaster Shuttle
This shuttle runs between the Coaster stop in SorrentoValley and campus (stopping at the Mandeville shuttle stop). It's schedule is timed around the arrival and departure of the Coaster so plan ahead and view the schedule.
Medical Campus Shuttle
This shuttle runs between the UCSD main campus and the UCSD Medical Hospital in Hillcrest. It is a fast/free way to get to Hillcrest if you happen to live around there or NorthPark. It operates the whole year.
On Campus Shuttles
There are also a couple shuttles that frequently loop around campus (clockwise and counterclockwise). They are only for the truly lazy though.