The Guardian is currently seeking volunteers to share stories about items they've kept after a breakup: "Tell us about the belongings your ex left behind. We'd like to hear from people about the times they kept after a break up and what they mean to them." Kind of sounds like what the Museum of Broken Relationships does (I wandered through the one in Los Angeles years ago and just found it depressing, to be honest.)
The Guardian further explain their project and what they are looking for:
We'd love to hear from you about the thing your ex left behind when you broke up, why you've kept it instead of giving it back, and what it still means to you.
If you are over 18 and want to participate, go here and fill out the form. Personally, I tend to not keep things after a breakup – I typically find leftover physical objects to be painful reminders of what didn't work out, so I don't keep them, and thus wouldn't have much to contribute to The Guardian's project.
The only thing I have from one pretty awful breakup is a custom-felt cowboy hat from Catalena Hatters in Bryan, Texas. I only kept it because my son is an actor and I thought he might be able to use it sometime in a scene if he ever got to play a cowboy. It no longer has any sentimental value, and it's been long enough post-breakup that it doesn't even remind me of the pain of that relationship anymore.