It depends on how much time you have to set up the shot. I would leave the camera in Program mode by default to catch shots where I don't have time to modify any settings.
If I have a little more time I would go for one of the scene modes as most cameras will do a pretty good job, e.g. landscape mode should give teh AF system a head start to focus in the distance, preferring a small aperture but not at the expense of a shutter speed that is too slow to eliminate handheld blur.
If I have some time to set the shot up I will go for aperture or shutter speed priority depending on the situation, and time allowing use exposure compensation based on the histogram information to get the image I want.
When using an external flash I will use aperture priority to control the ambient light/flash balance.
Only in very low light conditions (where exposure compensation doesn't have enough reach and the meter gets confused) will I use manual mode.