There are fancy fog-free mirrors or de-fogging sprays out there. While they are fun gadgets, there is no need to spend mucho dinero on them!
Make your own fog-free mirror. Pick up a cheap mirror anywhere (I love the dollar store for cheap mirrors, personally) and simply spread liquid soap on the glass completely with a cloth. Just polish it dry with another cloth, and voila! It lasts for quite a while and is free! Can't beat that, right?
Another tip while I'm thinking of it...
We have glass shower doors that always get water spots on them. I've learned that if I take my soapy/shampoo-y/conditioner-y hands and wipe the doors down while in the shower (then rinse thoroughly), it keeps water residue from building up, and keeps your doors clear and clean. That way you don't have to scrub them down after the fact! Pretty simple, eh?
Give it a try, and happy savings to you :)
(thanks to the Tightwad Gazette for the mirror tip)