Depends on what you are trying to achieve. (Actually this question has been asked to death, but nevermind.)
M = fully manual, and you have an idea of what aperture and shutter speed combination to use. Depends on experience.
A/Av = you control the aperture, meaning you are concerned more on achieving a certain depth-of-field effect and letting the computer do the rest.
S/Tv = you control the shutter speed, useful when you need at least a certain shutter speed to achieve what you want, e.g. freezing motion, achieve panning shots, do long exposure shots, etc.
P = as some say, "Professional" mode...haha...:sweat:
All other modes automatic modes (sports, macro, portrait, etc.) follow some pre-defined rule (e.g. sports = highest shutter speed possible without introducing handshake; see your camera manual for details) so there's very little control except when to press the shutter release.