I despise the smell of litter boxes. Even when cleaned well, the smell of cat litter can be overwhelming. It's ok if you live in a large house where you can dedicate a utility room, garage, or basement to the litter box. In an apartment, it is often impossible to keep a litter box out of smells reach.
For that reason, I made this simple litter box exhaust, which draws a small amount of air out of a covered litter box, and blows it outside. The computer fan draws just enough air to keep odors from escaping the box. The hot/cold air loss to the exterior seemed to be pretty minimal, because there is no noticeable change in heating/cooling costs. It works so well that people would be surprised that there were cats in the apartment.
The computer fan is rated at 0.13A, so it could easily be run off batteries being charged from a small solar panel outside. This instructable shows how to do just that: http://www.instructables.com/id/The-Amazing-Solar-Powered-Fan-A-Green-Gadget/
Cats are generally freaked out by noise and weird stuff in the litter box. The fan is so quite, and far enough away from the litter box, that the cats did not care in the least bit. They were actually a little curious as to the dryer hose sticking in the box.
I built this system years ago, but was prompted to put it up after seeing this: http://hackaday.com/2008/09/16/hack-your-littler-box/
The bathroom fan seems like overkill, especially considering the fact that they cannot leave it on all the time.
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Step 1: Materials
2. Plastic dryer hose
3. Sheet of Lexan
4. 2 Plastic cups that fit about 3/4 of the way into the dryer hose
5. Outdoor electrical junction box (which computer fan fits inside of)
8. 12 Volt wall power adapter