The previous post contains techniques you probably should keep in mind – but more that when you disregard the suggestions, you do so for a reason and/or with panache.
Never in the middle – except...
The case against putting something in the centre falls apart somewhat if the focus is asymmetrical. The more irregular the shape, the less it seems to matter.
If it's a portrait, or some other controlled environment where the background won't add anything to the shot, then having the primary subject(s) off to one edge may make the picture unnecessarily unbalanced.
Depending on your camera/lens, the border of a picture may also suffer from distortion (bending of the image), or vignetting (darkening of the image). I almost hesitate to mention this, as it only really happens at the extreme edges.
Most of the Picture?
As with the above, if the subject is interesting enough, you can probably get away with it taking up most of the space.
Conversely, if the background is dull, it's best to be rid as much of it as possible - especially when using a point and shoot camera - as it will likely be almost in focus as well.
There's a few ways you can get these kind of shots to work.
1) Be creative when cropping the shot. People are used to seeing the whole of something. It also helps to remove the (often dull) outer extremities.
2) Keep the flash off. Natural light makes things more dynamic. Work with it, not against it.
You won't get shadows like that with the flash on
3) (D)SLR cameras – Selective focus. One of the biggest strengths of these cameras is to have only small portion of your subject showing detail. You keep the colour and shape, but the eye isn't overwhelmed with where to look.