Split Lighting: Split lighting splits the face in half - with light! One half of the subjects face is lit while the other side is in shadows. The lighting set up for split lighting looks like this:
And a photo taken with split lighting looks like this:
Loop Lighting: This lighting technique creates small shadows on a subjects nose and cheeks, on either the left of right side of the subjects face. He's what the setup looks like:
And here is what loop lighting looks like on a subject, note that the light is places slightly higher then the subjects head, and the shadow on his left cheek and nose.
Rembrandt Lighting: Rembrandt lighting (named after the painter) is a type of lighting that leaves a a same triangle of light on one side of the face while the other half is well lit. Here's a Rembrandt lighting set up:
Now here's a photo of a subject being lit with Rembrandt lighting. Check out the triangle of light on the left side of the face.
Butterfly Lighting: Butterfly lighting is created by placing a light directly above and behind the camera. It creates a butterfly-like shadow on a persons face and is very flattering. Here's the setup:
Here's what butterfly lighting looks like on a subject, note the butterfly like shadow.
Broad lighting: In broad lighting, the subject turns their face slightly away from the camera, broadening the face. The light comes in a slight angle. Here's an example of the setup:
Here's an example of broad lighting, look at how it broadens the face: