Laura, that's funny! You mean things your partner can't see? Because of how they look or because of their emotional value?
I do keep an item that belonged to my husband for sentimental reasons. A long time ago we lived apart for study reasons and he gave me a big 80s sweatshirt to "hug" me from afar. I still have it and though I don't wear it anymore (my L.L. Bean fleece is warmer and comfier) I can't find the heart to part with it.