This is a great thread! Lots of interesting opinions here, I'll toss my two cents:
-- My wife and I both like to cook, so when we combined households we wound up with a lot of pots and pans, so I have quite a few to choose from. Over time, I found myself reaching for the cast iron more and more until that was pretty much all I was using. It wasn't a plan, it is just what I wound up doing because I liked the results. The cast iron just flat out works better. So that's the pan I use.
--But I still use a non-stick for eggs! Part of advantage is the curved sides of the non-stick make it easier to get the eggs out of the pan. Just tilt and slide. Can't do that with cast iron.
--Except for eggs and egg-like foods, Teflon pans are steaming heaps of garbage! You can't put them in the oven except at low temp, the fond doesn't develop, they have hot and cold spots, they don't hold heat, you have to be gentle, and they don't last. Someone mentioned they didn't like to pre-heat cast iron. In my experience, you really needs to pre-heat Teflon because the heat is so uneven, so you need time to get the whole pan up a uniform temperature. Eggs are a low heat food, so the Teflon works okay. But for higher heat stuff, the pan never becomes uniform and the food doesn't cook evenly. Completely unsuitable for everyday cooking.
--I almost always wash my cast-iron pan with water, and sometimes I use soap! The "don't wash with water" rule never made a lick of sense to me. All food, especially vegetables contain water. So there will always be some water in the pan when you cook, so if water itself was a problem our pans would have dissolved away years ago. The problem is water remaining on the pan when not in use. So I simply wash it out, dry thoroughly, and put it on a burner for a few minutes while I finish cleaning up the kitchen. Sometimes I put a coat of oil on it first, but sometimes I don't. Similarly, think about what soap is. It is basically water soluble fat, right? In the old days, they made soap from fat. Well, I use fat in my pan all the time. And I use water in my pan all the time. So I don't see why I can't use water soluble fat. I use soap sparingly of course, and most of the time I simply don't need to, it comes clean with a scrape and a rinse. I've never re-seasoned and the pan just keeps getting better.