I keep, and examine, and re-examine every kit I build. I still have models I built in the Sixties! Not all are on display, of course, but the best of the bunch sure are.
Each and every time I re-examine a model (they're not "kits" after we build them, eh?), I find something that I can improve on next time. Even if it's just a quick glance from across the room, it can help motivate me to do something different with my next build.
I love building kits, but I also love going back and looking at the models I've built and thinking about the technology and history they represent. I couldn't imagine selling, giving away, or storing my best works. Every model I've built in the 12 years I've lived here in Japan are on display in my small apartment.
My stuff in the States is indeed all in storage, but whenever I visit my hometown, I break 'em all out and relive the excitement!