Advantage 1 of Manual Focus:
Macro work, (best done using a tripod, seeing as any movement of the camera can effect the final look of the image). The narrow depth of field needed in marco shots mean that you need to be incredibly precise with focusing and being just a smidgeon out or having your camera choose to focus on the wrong part of your subject can completely ruin a shot as marco images are often very beautiful, sharp and unique.
Advantage 2 of Manual Focus:
Portraits. When shooting with a person the focus is always on the eyes, and Auto focus can often not do this. To make a perfect portrait the viewers eyes must be drawn to a certain part of the image, and manual focus does this perfectly.
Advantage 3 of Manual Focus:
Glass. When shooting through glass Auto focus often finds it hard to look at the image behind and focuses on the smudges and reflections on it.
Advantage 4 of manual Focus:
Shooting in dimly lit environments can be difficult for some cameras and lenses when it comes to focusing. Often, when shooting in dim light the camera will become confused as to where to focus and jitter around alot, still not know what you need, this is where manual focusing comes in handy.