This is an interesting question with a couple of possible answers. One of the things that you need to keep in mind is that stone tiles are heavy. For 1/2″ thick travertine tile you are looking at about 6 lbs per square foot. With that in mind, it is important to make sure your base is strong. If you are installing over a wood sub-floor, it is a good idea to use a second layer of either plywood or cement backer board. This will help to strengthen, and as a result, stabilize your sub-floor. Movement or unevenness in your sub-floor can lead to a difficult and inaccurate (read high corners) installation, not to mention cracking down the road.
You can pickup some extra plywood or backer board at most home improvement and home renovation stores.