I will be visiting Norway and Denmark on my next trip, and I was curious if there is border control when traveling by car or train or not. I'm non-European holding short-term Schengen.
Generally, as Norway and Denmark as both part of the Schengen area, a passport should not be required - however at the time of writing (Jul 2017) security measures are still increased and border control checks in force between many of the Nordic countries.
If you travel by train (without ferry crossing): you'll be traveling from Norway via Sweden to Denmark - border controls were in force until recently between Sweden and Denmark with a passport check taking place on the train. While these have ended, spot checks do still happen frequently (form personal experience).
Traveling by car, you will need to either take the ferry from Norway to Denmark or drive through Sweden. Driving through Sweden the situation is similar as when going through Sweden by train.
Taking the ferry (whether with or without vehicle, i.e. by car or taking trains to and from the ferry), you will need to carry some form ID (incl. date of birth and photo - exact details see ferry operators ColorLine, fjordline, StenaLine) and it will be checked.
In conclusion: some of the border controls re-introduced in 2015 during the refugee crisis may have been abolished, but you're still likely to face an ID check - be it as a definite on the ferry or when encountering one of the very frequent spot checks on trains or when crossing borders by car.