I guess that obi completeness counts for this topic... there are some games that are really hard to find compete with obi:

Kitchen Panic (PS): I've never seen a complete copy for sale/auction. I searched for a while trying to find one, but I found a great deal on an incomplete copy and went for it. Great game BTW!

Ningyo no Rakuin (PS): Another uncommon/semi-rare game that I've had trouble finding with the obi intact. It's easier to find sealed than Kitchen Panic, though.

Those are the only examples I can think of offhand.