You may have to wait for the most popular one. Delicious Monster is supposed to be close to releasing their app "Delicious Library." It's available now as a Desktop app and you'd probably be good to use that if you're on a Mac, but the iPhone app will be a "sidekick" style app that would allow for syncing back to your main application for managing check-ins and outs of your DVD. The full functionality is not yet listed, but knowing the types of apps they've developed in the past it should be pretty good. The only other solution that I can think of that would be far more generic would be "iOwn" or "iOwn Lite" as a tool to catalog your belongings in general.
I suggest iOwn. You can organize it like so: places- home, work, car; rooms- office, bed room, living room; container- blue tub, DVD rack, jewelry case; then the items within the container. Also stores pictures, warrenty info, and has free online backup
