I have taken a great interest in cosmology and quantum theory but I don't have the background to grasp the equations which relate to them.  Can anyone recommend some good books to help me understand the current cosmological models?  I have read The Big Bang, A Brief History of Time, and a few others...

Try these:

The Universe in a Nutshell by Hawking

Once Upon a Universe: Not so Grimm Tales of Cosmology by Robert Gilmore

Complete Idiots Guide to Theories of the Universe by Gary Moring

Complete Idiots Guide To Understanding Einstein by Gary Moring

No math test required.  Just cover the CIGT books with paper or a magazine and no one will be the wiser, save yourself!

L

A good, and very readable, start (for anyone) would be:

The Complete Idiot's Guide to Theories of the Universe, by Gary F. Moring.