CouchSurfing connects travellers with locals who have a spare couch/bed to sleep on. Not only is this a great way to save money, it is also a great way to introduce you to a local, and to really see how a local lives by staying in their home. I have used CouchSurfing myself and I can personally recommend the experience (check my CouchSurfing profile.)
With CouchSurfing you can search for accommodation in the city you are visiting and stay with a local host. If you are not on the road yourself you can host visitors at your place.