Here are two examples of bistable flip flops which can be toggled between states with a single push button. When the button is pressed, the capacitor connected to the base of the conducting transistor will charge to a slightly higher voltage. When the button is released, the same capacitor will discharge back to the previous voltage causing the transistor to turn off. The rising voltage at the collector of the transistor that is turning off causes the opposite transistor to turn on and the circuit remains in a stable state until the next time the button is pressed and released. Note that in the LED circuit, the base current from the conducting transistor flows through the LED that should be off, causing it to illuminate dimly. The base current is around 1 mA and adding a 1K resistor in parallel with the LED will reduce the voltage to about 1 volt which should be low enough to ensure the LED turns completely off.
circuit from http://www.bowdenshobbycircuits.info/page9.htm#toggle.gif