What do I do if there are only two wires coming from my ceiling electrical box?
The 3 wires are normally hot, neutral, and ground. It sounds like your home doesn't have a ground wire.

From Wikipedia: 


  Equipment earthing conductors provide an electrical connection between non-current-carrying metallic parts of equipment and the earth. The reason for doing this according to the U.S. National Electrical Code (NEC), is to limit the voltage imposed by lightning, line surges, and contact with higher voltage lines. The equipment earthing conductor is usually also used as the equipment bonding conductor (see below).
  
  Equipment bonding conductors provide a low impedance path between non-current-carrying metallic parts of equipment and one of the conductors of that electrical system's source, so that if a part becomes energized for any reason, such as a frayed or damaged conductor, a short circuit will occur and operate a circuit breaker or fuse to disconnect the faulted circuit. By bonding (interconnecting) all exposed non-current carrying metal objects together, they should remain near the same potential thus reducing the chance of a shock. This is especially important in bathrooms where one may be in contact with several different metallic systems such as supply and drain pipes and appliance frames. The equipment bonding conductor is usually also used as the equipment earthing conductor (see above).


If the box is metallic, there's a chance it may still be grounded, even though there is no wire. There's an answer to a similar question that describes how to check if a box is grounded.



If the box is grounded..

If the box is grounded, then you can connect the ground wire from the fan directly to the box, and the fan will be grounded.

If not..

If the box is not grounded, you have two choices:


Run a ground to the box. This would mean running a new wire back to the panel (could be bare copper, but if you're doing the work may be better just to run a new wire - 14/3 would be the best), which could mean opening up drywall. 
Wire the fan without ground. This is slightly dangerous, but not moreso than the when the previous fixture was there -- except that people do touch fans to control them. If something ever happens to cause the fixture to become energized (eg a frayed wire inside), someone who touches it will likely be shocked (which can cause serious injuries and even death).  


Personally, if I was unable to get a ground to the box, I'd probably use a fan that was remote controlled so no one ever has a need to touch it (get a fan either with no pull strings/controls, or cut the cords off so no one is tempted to touch them). The wall switch can be left in to control overall power, and the remote used to switch light/fan speed, or the wall switch can be removed so the power is permanently on and the remote is used for everything.

In any case, you should connect the fan's ground wire to the box, so that at least the fan body and box are bonded (at the same electrical potential). 



Bootleg Ground

DO NOT CONNECT GROUND AND NEUTRAL in the box. This is sometimes called a "bootleg ground" and is not only pointless, but actually very dangerous. If the neutral wire ever has a fault ANYWHERE, in addition to the fixture simply not working, it becomes energized and you can be shocked if you touch it (as you likely would to, say, check if the light bulb was burnt out).