Arduino Analog Input Oscillating
It seems you haven't connected the circuit ground to the Arduino ground.  This is essential to complete the circuit between your breadboard and the Arduino.  Without the ground connection the electrons that you send to the Arduino have no way of getting back again.
Here's a couple of diagrams that I drew for another question which deals with the Arduino driving a remote device, but the theory holds true no matter which way around it is.

In that diagram the red arrows (not the aerial display team I hasten to add) represent the connection between your breadboard circuit and the Arduino.  Without the ground connection there is no circuit, and a circuit is always needed for current to flow (and hence your signal).  With the ground connection the red arrows become a loop which allows the current to flow and transfer your signal.