You can get "voltage doublers" which are simple circuits that charge and discharge a capacitor to do what you want. It's often used for adding to the positive voltage but it can easily be subtracted from the negative voltage too. It may also be known as a DC/DC converter.
For small power requirements (like a milliamp or so) a MAX232 chip has a neat voltage-doubler-and-inverter circuit on board. That's actually my choice these days to get a reference voltage or opamp supply below zero volts.