When you should not use Auto-Tune
You should definitely not use Auto-Tune when you are working with a great singer backed mostly by acoustic instruments, or electric instruments such as the electric guitar or (genuine) Fender Rhodes piano.
The reason for this is that if you have a great singer, what could you possibly want to do to meddle with their performance? Tuning is subjective and there is no such thing as 'accurate'. Accuracy in tuning means perfect alignment to the even-tempered scale that is a compromise already. Take away the subtle shadings of pitch that a great singer will use, and you have taken much of the artistry out of the performance.
If you are working with a singer who is dreadfully out of tune, Auto-Tune can't offer much help. In order to recognize which notes the singer intends to sing, they must be performed with an accuracy of better than half of the step between adjacent notes. For some notes in the scale, this means an accuracy of better than a quarter of a tone. Manual retuning will be necessary.
When you should use Auto-Tune
When you have a singer who is a little less than perfect, backed by electronic or digital instruments that are always exactly in tune, Auto-Tune will probably help. The comparison between the perfect tuning of the instruments against the slight approximations of the singer is often uncomfortable to listen to. Auto-Tune can make the singer as accurate as the instruments.
When you should carefully consider whether to use Auto-Tune
When you need to get the work done quickly. If you need to get the work out of the door in a hurry, and often there are occasions when this is necessary, Auto-Tune can help speed things up, rather than spend time on retakes.
In summary, Auto-Tune and other pitch correction software can be very useful. But be careful that they don't take the soul out of the performance.