Premise
Clipping brushes should be (but usually aren't) used in many places,
to fix bugs, make moving easier, etc. In this tutorial, I'm going
to try and show you how to use clipping brushes to make your levels
better.
What is a clipping brush?
A clipping brush is a brush with the "clip" texture assigned
to it. What it does is it keeps players and monsters from going
inside of it, while not being rendered and allowing bullets through.
Basic Use
The most common (and basic) use of a clipping brush is to prevent
bugs in a level. Many times, the player can fall in between two
solids and get stuck between them, clipping brushes can solve this.

Possible Problem Area

Cover with Clipping Brush
Covering Details
Another way to use a clipping brush is to cover a detail to facilitate
(I like that word) movement. To do this, simply cover a detail with
a clipping brush, this will prevent players from possibly getting
stuck on it.

Cover Details
Advanced Use
While the above methods are the most used (and probably the reasons
the game creators allowed clipping brushes) there are other ways to
use a clipping brush. One thing that really helps (but not many mappers
do) is to "smooth" the edges, so the player doesn't get caught on
the clipping brush itself. This is especially good on details on walls,
chairs, and many other things. (The desk lamp example isn't a very
good one, but it was all I could think of...)

A "Smooth" Clipping Brush
Misc.
Remember, since clipping brushes aren't rendered, they won't add
to the r_speeds, so you can make them as complex as you want (to a
certain extent, that is...). Also remember NOT to use them as invisible
stairs, etc., as those are just plain annoying and detract from levels
greatly.
Also, ALWAYS remember to cover the part of a sky brush that's showing
with a clipping brush, this will prevent people from gauss jumping
into the sky (which, although fun, is bad).