I think the power of the white mat to show artwork to best effect is two-fold. First, the brightness of the white draws the attention of the eye. Second, the mat acts as a kind of a palate cleanser for the eyes between viewing the rest of the room and viewing the artwork.
Additionally, the mat serves to protect the artwork by separating it from the glass (if any moisture gets in the frame, the photo or other art will stick to the glass!) and by providing thickness to help with mounting without use of damaging adhesives. So, aesthetics aside, you should use them to protect your investments.
And upon reflection, I got these frames for 50% off at Hobby Lobby so they were $3 each and spent $1.10 each for the mats (I bought 20 at once from Amazon). I think I spent at least $4 on my 8x10 frames so I totally should have done this to begin with.
A very quick (less than 20 minutes for more than a dozen frames) and relatively cheap change can dramatically alter the look of a room. When I get the bedding I am working on finished (stay tuned for tutorials), I'll show the broader picture of the room and the effect this has.
Go forth and wield the power of the white mat.