I've read a bunch of on-line 3D graphics tutorials and each keeps referring to the concept of unit vectors. Now I know what a unit vector is and how to make a vector into a unit vector. My questions is, for what purposes do you NEED to use unit vectors and when don't you need to use them (i.e. translations, rotations, plane-line intersection, etc)?

Thanks in advance for your help.

You usually use a unit vector to avoid a division by the vector magnitude, since a unit vector has a magnitude of 1.

For example, if we were to define a directional light as a vector, v, and a vertex with normal, n, the light intensity at the vertex would be (v . n)/(|v|*|n|). If |v| and |n| are both equal to one (they are unit vectors), we could omit the costly divide, and just calculate light as v . n.