San Francisco is a great place to develop a newspaper-reading habit. As a densely populated, politically aware, relatively commute-friendly city, San Francisco has been able to provide enough readership to support several newspapers. Some are local, some aren't.
Daily Newspapers
San Francisco Chronicle - major newspaper, headquartered near downtown. You can buy it for half-price from vendors in most BART stations.
San Francisco Examiner - free newspaper, the SF Chronicle's closest local competitor. Too thin, but it's good if you want to keep up to date without buying.
The Independent - free newspaper, rarer. Very similar content to the Examiner. It even runs Examiner ads sometimes (that's kind of shady, isn't it?)
Alternative Weekly Newspapers
East Bay Express - can only be found around the financial district and Embarcadero (i.e. where people might take BART to the East Bay)
Other
The Onion - the nation's parody newspaper came to San Francisco in 2005
