A Recreational Aviation licence (RA-Aus) is much cheaper to get than a full PPL, but it does have it's restrictions.  The age and medical requirements are also less stringent - if you're over 15 and fit enough to drive a car, you can fly RA.

An RA licence can be obtained with approximately 20 hours of instruction, and will allow you to fly a range of RA registered ultralight or light sports aircraft within a 25 nautical mile radius of your departure airfield, outside Class  A, C or D airspace.  A cross country endorsement will allow you to fly further afield, but still not within the above airspace classes.  

RA registered aircraft have maximum take off weight limits of 300kg (single seat) and 650kg (two seat).  Speed limits also apply - typically top speeds of less than 110 Knots.  Examples of RA aircraft include some of the Jabiru range, the Lightwing range, Evektor Sportstar and the Zenith.  

Many of the aircraft in the RA class can also be VH registered.  

A range of regulations apply to the classes of aircraft depending on whether they are home-built, experimental, factory built kits, or fully factory assembled.  A great website for RA pilots, with heaps of useful information, is Recreational Aviation Australia Inc.