How often should I clean my coffeepot, and what is the preferred method? We use a typical drip coffee maker with a thermos-type pot. Naturally I rinse the pot and filter holder every day, but how often do I need to clean it more thoroughly? I've heard that it is bad to use soap and water, but is that just an old-wives tale, maybe out of fear that it could leave a soapy residue? Once a month or so, I'll run a few cups of white vinegar through it, which seems to improve the flavor a lot, but is a surprisingly expensive proposition. Any suggestions on frequency and method?
Your specific coffee maker should have instructions.  Mine says every 30-40 pots you brew and it uses the same typical white vinegar method.

I do think it's a little expensive - you basically drain a whole bottle of vinegar.  However, compared to the cost of the machine and, more so, the cost of the coffee it's not a bad deal at all.