Air handler runs but outside fan does not. No buzzing, no noise, just does not run. Power on, no breakers flipped off. This happened suddenly with no warning.

The thermostat provide 24 volts to the compressor/Fan's contactors coil. If not, may be a thermostat or control wiring problem, if you have 24 volts at the contactor coil, and it doesn't energize, Contactor is Bad.

You will need to test the contactor with a volt meter to see if it is getting 24-28 volts ac to coil and 240 volts to main wires coming in. Without a meter you cannot tell what the problem is. On a straight AC unit you will have two control wires going to contactor, the big relay where the power supply goes to it and the thin thermostat wires that lead to the coil. Push it in with a screwdriver and if it comes on then you have main power and just the coil is not pulling in. Do not just change this without first checking it out or you will waste time and money. Here are some wiring diagrams: https://dl.dropbox.com/u/8010163/AC%20Wiring%20Diagrams.zip
https://dl.dropbox.com/u/8010163/How%20to%20use%20Test%20Equipment%20Service%20Manu al.pdf