After a relationship ends, whether a person is dumped or if they are the one doing the breaking up, people often keep mementos of their ex. Since this relationship once meant something to both parties, this is a normal response.
People do this for several reasons. The first is the obvious...love. If on the wrong side of the breakup, you could be left feeling crushed that the person you once loved broke your heart. It is natural to keep the things this person gave you to hold on to that love. Some people do it out of hopes that one day you will get back together. Even if it doesn't happen right away, people hold on to those tokens because they hope that some day their paths will cross and that spark will still be there. Then you can display those gifts again or return them to their rightful owner and all will be as it should. Whether this ends up the case or not, some people just need that glimmer of hope.
Another reason people hold on to their "ex-files" is because people like to reflect on their past, whether it brought happy memories or devastating nightmares. Some like to think about all the fun things they did with the person who once meant so much to them. Other people like to think about the not-so-happy times, just to remind themselves why they are not with that person. What seperates people from other living creatures in this world is the brain. And memories are a huge part of that organ. So why not use it?
Humans learn from their past. By looking through old photos, you'll get a quick history lesson on your exes and remember what you are looking for in a person and what you want to avoid. For instance, an ex boyfriend or girlfriend could have been very emotional or clung to you like rancid sauce on spaghetti. You have since rinsed yourself off and started over, knowing to look for clues of that kind of behavior. If little things set a person off, you steer clear. Even if you slip up and get caught up in a relationship that isn't for you, a glimpse of past flames will remind you what real love is like. It could motivate you to get out and find something better.
Likewise, when people reflect on good things about a relationship, we learn to look for those same qualities in someone else. Though an ex may have had flaws, they had some admirable traits as well. They might have been laid back, or made you laugh a lot, for example. So now you know to look for someone who doesn't sweat the small stuff and has a sense of humor.
Lastly, our past helps mold us into our future selves. By looking at mementos and pictures we remember where we came from and how far we've gotten in life. It helps us appreciate the present that much more.
So I say keep those "Ex-Files". They might be things from the past, but they mean so much more than that. As long as they don't hinder your future, they are ok to store away until you need that push to either make a change for the better or appreciate what you've got.