Scanline - Fastest approach. Each polygon is projected point by point onto the view screen.
A zbuffer is generally used to deal with objects that obscure other objects.
Can't do reflection or refraction except as a hack. Can do shadows.
Ray Tracing:
Much slower than scanline but produces much more realistic lighting. Best for highly reflective
(as opposed to diffuse) surfaces. Does much better job on shadows than scanline.
Radiosity: A more advanced type of rendering that is good for diffuse surfaces.
It is available in the mental-ray renderer in Maya but is tricky to use (so don't use it).