Yes, it is possible to visit the eerste hulp afdeling (accident and emergency department) in a hospital without a referral. If the situation allows, it is best to contact your huisarts (GP) or your local out-of-hours huisartsenpost (GP centres that open outside office hours) phone line first. Many problems can be treated by a GP without the need to visit the accident and emergency department in a hospital.
For life-threatening situations, you can call 112. This number works for emergencies throughout continental Europe (Great Britain has a different emergency number).
In the Netherlands, you cannot call an ambulance yourself. Only your huisarts (GP) or the emergency services can call an ambulance.