A picture has many features, so unless you narrow yourself to one, like average brightness, you are dealing with an n-dimensional problem space.
If I asked you to assign a single integer to the cities of the world, so I could tell which ones are close, the results wouldn't be great. You might, for example, choose time zone as your single integer and get good results with certain cities. However, a city near the north pole and another city near the south pole can also be in the same time zone, even though they are at opposite ends of the planet. If I let you use two integers, you could get very good results with latitude and longitude. The problem is the same for image similarity.
All that said, there are algorithms that try to cluster similar images together, which is effectively what you're asking for. This is what happens when you do face detection with Picasa. Even before you identify any faces, it clusters similar ones together so that it's easy to go through a set of similar faces and give most of them the same name.
There is also a technique called Principle Component Analysis, which lets you reduce n-dimensional data down to any smaller number of dimensions. So a picture with n features could be reduced to one feature. However, this is still not the best approach for comparing images.
