1 - For a piece of art that is not hung over furniture, the general rule of thumb is to hang it so the center is at 60" high. Basically, your eyes should be around the center. If people in your home are exceptionally tall or short, you might want to vary just slightly. Going with average height is going to look best to most people.
2 - If the art is hung over a piece of furniture you'll want it to appear to be part of the furniture display. If it is hung much higher, it will appear disconnected.
The next two rules are the exceptions to rule two.
3 - If the art ends up closer to the ceiling than the piece of furniture, you'll want to split the difference between the two and center the art between the ceiling and furniture. You don't want the art to be closer to the ceiling or again, it will look disconnected from the furniture.
4 - The next exception is when you have a piece of furniture that something will be on such as a daybed without a back. In the case below, the pillows act as part of the furniture, in effect extending the height of the day bed. As you can see, the art is actually closer to the ceiling here. But with the pillows, the difference is less. The bottom line is, in cases like this, you'll need to think the whole design through before hanging your art.
That's really all there is to it. I hope this helps you create beautiful displays in your home!