Reged: 06/01/04
Posts: 7013
Loc: Maine (IBS-A stable since July '05!)
Double boilers are typically used for cooking things that would normally scorch if put directly over the burner... you see it a lot in recipes that call for melting chocolate, but also a lot of creamier sauces, and some recipes that call for eggs to be incorporated, call for one too.
I have crappy nonstick pans, so I'll skip that one.
Cast-iron pans are kind of a pain to clean, but I don't think anything beats them as far as heat conductivity and even cooking. I use mine when I'm roasting meat/poultry - it can be seared on the stovetop, and then tossed in the oven to roast - and for some "old-fashioned" bread/cake recipes, like cornbread. Plus, they're typically pretty cheap, and if you take care of them, they'll last a lifetime, unlike a lot of nonstick pans.
Bonus - I just learned this this past weekend: you can actually thaw frozen meat in them. Put it on the stove - no heat - and put the frozen meat in it. Cast iron acts like a heat sink (cold sink?) and apparently will thaw meat faster than any other method except the microwave.
Other kitchen things I can't live without: my slow-cooker, my bread machine, and a GOOD set of knives. On MY wishlist this year is an ice-cream maker.