Sometimes mountains won't have trails or recorded routes simply because they don't get enough traffic that a trail will be created. Not every mountain has a recorded routes simply because people haven't written them down in an easily accessible place for everyone yet.
For example, consider this Google Earth picture of a mountain. (Larger image)
There are no trails from the viewpoint up to the summit and everything between the viewer and the summit is public land. If one were to say, "Wow that looks like a cool mountain, let's go climb that" are there any general rules of thumb as to what to look for when planning a route?