My great-grandfather's folding bowie, a beautiful knife with lots of history.
My family's "starter" knife is another one I'd hate to loose. It's a small bowie, made by a now dead Argentinian knifemaker with Swedish steel, the pommel has a lion's head. Since my great-grandfather got it as a gift, it has been the first knife for every male boy in the family, once you learned your basics with it you had to pass it on. The last recipient was my little brother (now 17). Kids do awfull things to the blade, but our tradition is not to fix them right away, they are left like that until a new boy is born, and then the previous owner fixes it for him. It will be my son's first blade, and with any luck it will be his son's first blade.
My other great-grandfather passed on a very nice small collection of Spanish penknives, I'd hate to loose them, too.
And finally, I'd really hate to loose my first good knife, a custom given to me by my dad that has the perfect design for me and has been on my side everywhere.
Loosing some of my expensive knives would really bother me, but I would trade them all for the ones that have emotional meaning in a heartbeat. You just can't put a price on them.