The tram is free between South Terrace and the Entertainment Centre (-where you can get a $2 Park and Ride), as well as within Glenelg.
There are also free connector services around the perimeter of Adelaide City, clockwise and counter clockwise
Public transport is also a lot cheaper if you buy a multi- trip ticket or get a Metro Card (like an Oyster card).
Tickets are also a great deal cheaper between 9 am and 3 pm
PT is free for those with a concession, student or seniors card at off peak times; all weekend and all Public Holidays
Public Transport to major events at the Adelaide Oval, Entertainment Centre, and on New Years Eve etc etc is free
Tickets will give you an unlimited number of transfers between Bus, Train, Tram and O'Bahn within a two hour period
The O'Bahn is a dedicated express bus track offering a 100km an hour service (approx every 5 to 10 minutes during the day). It will get you into the heart of the city in about 10 minutes, and it is being extended for an even quicker service.
However, the buses themselves are not dedicated to running only on the track. -They become flexible suburban services at either end of the track.
The O'Bahn interchanges offer Free Parking (and free lock ups for pushbikes ) at Modbury, Paradise and Klemzig.