AC Transit actually runs a bunch of buses from SF to Berkeley, Emeryville, Albany, Oakland, etc. Here's the full list:
Transit 511: Schedules & Route Maps - AC Transit (Transbay service) Routes
They follow the old streetcar lines that used to cross into SF on the lower deck of the Bay Bridge. They're a great way to get over there assuming you need to go somewhere near the Transbay terminal downtown (and need to come from somewhere near a stop)---it's hard to beat SF to Berkeley in 15 minutes at rush hour, even on BART. *BUT* they aren't much/any cheaper than BART---$4 a pop if you ride once in a while, or $130ish a month if you commute regularly. (That does cover unlimited local bus rides too, so it's a decent deal if you use the local bus, but otherwise it's about the same as BART for many areas.) Also, many (though not all) are commute-hour only.