There will be regular service until 8 p.m., and then BART will run special extended service from 8 p.m. to 3 a.m. During that time, BART will use a stop-skipping schedule to minimize overcrowding. Pittsburg/Bay Point and Richmond trains will not stop at Embarcadero; Dublin/Pleasanton and Fremont trains will not stop at Montgomery Street, and will not stop at West Oakland after the midnight fireworks show in San Francisco. Check the BART announcement for full details. BART will not be free.
Muni
Free rides for everyone! SFMTA will have free rides from 8 p.m. on Saturday to 5 a.m. on Sunday, Jan. 1. Do not tag your Clipper Card during this time or it will be charged. Some extra service is scheduled, though there is currently no rerouting planned or street closures. Check the SFMTA for information on all route changes.
Caltrain
Caltrain will also have free service starting at 8 p.m. on Dec. 31. Post-fireworks, there will be service at 12:45 a.m., 1: 15 a.m., 1:45 a.m., and 2:15 a.m. leaving from the main San Francisco station at Fourth and King streets.
AC Transit
AC Transit rides will be free from 8 p.m. to 5 a.m. And you may want to check the schedule for their All Nighter bus lines.
SamTrans
All buses will be free from 8 p.m. Saturday to 5 a.m. on Sunday. (Redi-Wheels, the paratransit provider for the county, will also be offering free rides to its users during that time.) SamTrans will run a regular Saturday schedule on New Year's Eve and a Sunday schedule on New Year's Day.
VTA
VTA rides will also be free from 8 p.m. to 5 a.m. -- standard partying hours. There will be extended late-night service for light rail (Alum Rock-Santa Teresa and Mountain View-Winchester lines) and for the express line 180/181 (to the Fremont BART station). Check the VTA site for last trip times.
Golden Gate Transit and Ferry
If you live in the North Bay, well, you have other things going for you -- but no free rides. Service will be on a regular Saturday schedule on Saturday and on a holiday/Sunday schedule on Sunday and Monday.