Q:

How do I extrude perpendicular to a plane NOT oriented along X, Y or Z?

I have a elbow pipe joint and I want to extrude the selected edges out to extend the pipe: 

However, there is no convenient axis to restrict movement to.
Any ideas?

A:

Press F to fill the face with an n-gon and then extrude.
Once a face exists the extrusion can happen along the normal of that face.
If you then want to move the face along that axis again you can change the transformation widget to the 'Normal' axis:

Allowing you to move like so either by using the widget pictured...

or by pressing G,Z,Z.
You can then delete the face after the extrusion is complete via X.

A:

When extruding an open edge loop the move operation is free of any axis constraints, while extruding from a face will be constrained along the face normal.
The quick solution is to fill in the face then extrude and delete the face.

