Anisotropic: metal, compact discs (cd's) or hair

Blinn: metal surfaces but I end up using blinn for almost every object type (basically blinn can be modified to be used for almost anything at all.)

Hair Tube Shader: The shader attributes are similar to the anisotropic shader in terms of the the specularity control... besides that it's the basic Blinn shader attributes, with a few extras.
*Maya Help files say:
If you convert your Paint Effects hair system to polygons, then a default Paint Effects tube shader is created. The former color attributes you set in the hair system are converted to the tube shader, but there is no construction history for these attributes. Any shading changes you want to make after you convert Paint Effects to polygons must be done using the tube shader.

Lambert: nothing. lol well not nothing, i guess you can use it for chalk, or really dull objects... I recomend just using the Blinn shader then turn down all the specularity and reflections, to get the same effect, just with more control.

Layered Shader: allows you to use different shader types, and stack them into layers much similar to how you would with photoshop layers

Ocean Shader: water, oceans. It's attributes control things like wave size, strength, speed, etc... it's pretty straight forward for the most part.

Phong: Plastic, or tiles, or anything that has a high gloss look to it.

Phong E: same as Phong except with different specularity controls. not really any difference...just personal preference.

Ramp Shader: allows you to create cartoon type shaders, or subtle rim-light effects, etc... I usually just use it for cartoon characters if you want it to look like 2d animation/renders. But it can also be used to control the colours falloff, etc without having to deal with the sampler info node etc.

Shading Map: is used for custom shaders. I used to use it for custom cartoon shader before the ramp shader came standard with maya. You can also connect other shaders to this node such as lambert, blinn, etc...

Surface Shader: is used for custom shaders as well, along with some render passes tricks, etc.
*edit* this is what the maya help files say:
Is a material (shader) that is a wrapper node, which means that you can connect any keyable attribute to this shading group, and then connect the shading group to an object. For example, you can connect an object's Translate Position to a Surface Shader's Out Color attribute to determine the object's color by the object's position.

Use Background: I have no idea, I never used this shader in my Life. I think it has something to do with compositing photo/film footage within the 3d scene. The object won't show up in a render, but it will take on shadows, and reflections, etc..
I'll have to research this shader more ... F1/help is my best friend, so is google :P