Much of it? Not even close. Here’s a map from 1914. Thin red lines are street cars: http://www.davidrumsey.com/luna/servlet/detail/RUMSEY~8~1~21...

These days we mostly have a combination of a few places connected to BART/Muni, and the rest handled by buses and trolleybuses, which are in general incredibly slow, because they get stuck in car traffic and make frequent long stops to load and unload passengers. There are a couple of cable cars, and one restored streetcar line, https://en.wikipedia.org/wiki/F_Market_%26_Wharves, but they’re mostly kept that way as tourist attractions and curiosities.