Collect QSL cards
Sharing your achievement of making a contact - known as a QSO - can be confirmed with the exchange of a post-card - or QSL Card - with the station you spoke to. Making a library of these contacts gives you a tangible connection to a station on the other side of the globe.
You'll need to log your contacts, and exchange contact information, or use a QSL Bureau or one of the many on-line services.