The 50 or so that are on "display" are housed on a remarkably ugly set of steel shelves in our study. My kids (both under 5) are remarkably good about respecting the space, and building/acquiring a proper cabinet is on my to do list.
The rest that are 'retired' are stored in big plastic 90L roller bins with clip-on lids. There are other (likely better) ways of secure storing (like custom hacked to shape polystyrene or foam in individual boxes), but this is efficient, doesn't seem to damage them, and it can fit bigger models in too (like a 1/72 C-130). Plus there's too many of them to be lavish with the more complicated storage methods.
If they travel anywhere for a show they get treated like this:
http://i50.photobucket.com/albums/f341/saylittle/packedmodels.jpg
Appropriate size heavy cardboard box, lined on the bottom with bubble wrap to stop them moving laterally, and foam to hold them in place as a backup, with bubble wrap laid over and the lid closed to keep them safe if they bounce. Stopping them moving in the box is the main thing. These guys are reasonably delicate, but managed an 80 mile each way trip to a recent airshow in the back of someones car with no drama. This box in particular is a Fed-Ex laptop courier, and the foam came with it which was handy.