I keep mine in the bottom drawer of my stove. I also keep my griddle plate there. (5 burner stove, came with griddle plate and grate for middle burner)

If I didn't have a drawer on my range, I would keep them with the rest of my pots and pans in a cabinet drawer.

I keep my largest pots, including Le Creuset dutch oven, in the pantry. The cast iron skillets go in the drawer with all the other pots and pans.

The cast iron skillets go into a drawer with my secondary skillets. The cocottes/dutch ovens go in the glass-fronted cabinets flanking the range.

Some people get tower etageres and display them. Something like this, but with dutch ovens:

Grand Tour etagere · More Info

My last stove was 8 burners and I kept my most used on top. This house is currently 5 burner 36" so everything is kept in drawers. Soon we will be back to a 48" and I expect the most used will end up back on top. The others will be vertical in deep low drawers with heavy duty slides.

I"ve got heavy duty wall mounted pot racks next to my stove. All my frypans hang there.

There are some ideas in this thread that I bookmarked:

http://ths.gardenweb.com/discussions/3413067/cast-iron-pan-storage-found-a-winner-method

I keep my LC Dutch ovens on shelves in the pantry. Cast iron skillets are hung from nails in the pantry as well. Handy but out of the way. I don't have that much good storage.

I keep my favorite LC out on the range because it was my first and a gift from my mom :) all the rest go in the drawers on either side of the range.

Mine lives on the turntable in my corner cabinet next to the stove. I always dry it over a low flame or in the still warm oven.

Most of mine are stored in the drawer of my range but I have quite a few and they won't all fit. The ceramic coated dutch oven goes in the drawer with my other pots, the smaller skillets/griddles type skillets go in the drawer with my other skillets. Everything else goes in the range drawer except the tea kettle which sits out on my stove top all the time.

My favorite way to store my skillets was to hang them on the side of a cabinet, but since reno that's not an option anymore. Now they are on an aftermarket wire shelf unit in a base cab. The dutch ovens are also in a base cabinet. The oversized giant skillet often gets left out on the cooktop. If that starts to bug me, I stick it in my lower oven so that it's out of the way. It's a beast to heft around though, so I'm prone to leaving it out.

All but the 10", which lives stovetop, are in open shelves right next to the range. I was worried about all that weight in drawers, but judging from the answers here my fears might have been unfounded.

FYI My low drawers are all heavy duty slides and the cabinets are sturdy.