I do keep some things, a picture here, a poem there. They were once happy memories, so I see no reason why I shouldn't keep them. Just because we don't belong together anymore doesn't mean I don't cherish the good times we had. Not that I stroll down memory lane often, but I just see no good reason to destroy beautiful memories.
I should mention that I'm married, but we're polyamarous, so that might be why I have less of an issue with it than others. I'm not sure if we were monogamous how my husband would feel. But that's not really something I need to worry about.