I have taken the bus now twice without paying. (To be clear, both times it wasn't my fault. The first time the coin slot was closed and the second time the coin slot was jammed by the guy who used it right before me. The bus driver did not know that the coin slot jammed nor did he care.) But I think it illustrates that many things seem to run on the honor system here with regard to buses, car registration, and media licenses.
On the buses in Århus (but not other Danish cities), the ticket machine is at the back of the bus where passengers also board. Then they put money into the machine to get a ticket or stamp their passes. Since the driver does not see the passengers pay, passengers can sometimes get a free ride.
Though there is a risk in doing this because sometimes there are plain-clothed and uniform bus company employees on the bus who check to see if passengers have paid. Those that don't get a hefty fine of 200 or 300 kroner ($40-60) so it's probably better to always pay it anyway.
An Italian housemate of mine brought his car from Italy and now uses it here. He has not registered it in Denmark because it's expensive. People get a grace period (of a couple months, I think) to do it. But there's no way of knowing when my housemate first entered Denmark. In the unlikely event he is stopped by the police, he plans to say he just arrived in Denmark so his grace period hasn't expired.
According to my lease, all Danish residents must pay a media license fee to the government once a year of about 2000 kroner ($400). It's required for anyone using a computer, radio, or TV. This is separate from the monthly fee to the internet service provider which supplies our house. My mentor, a Danish student helping me to settle in, told me not to pay the license fee. Likely no one will chase me down so I shouldn't pay it.