Symmetrical power supply circuit
This is called a virtual ground circuit.  And this one will not work in all applications - it's very limited in terms of the amount of current it can source or sink from the virtual ground.  For a simple audio amplifier running on a 9 volt battery, it's fine.  But for more demanding applications, it likely won't be sufficient.  A very simple improvement would be to add a single op-amp voltage follower (noninverting with unity gain) to act as a buffer on the GND line.  This would significantly improve the performance of the virtual ground.  I have used this technique on several different circuits myself, and it is quite effective.  Here is a page that covers several different methods for creating a virtual ground:

http://tangentsoft.net/elec/vgrounds.html