In Spain, plates are related to vehicle, not owner. When you transfer your vehicle, the plate goes with it. The "sticker" in your plates is what in the UK is known as "tax disc", and here it also a tax but it's enough if you carry the payment receipt with you and show it when requested.
Law-enforcement officers can check in their database any vehicle plate, and the database will tell them what make, model, colour and who the owner is. The only cases I can think of using fake plates for commiting crimes has been in terrorism -car bombs- in which the terrorist put fake plates in stolen cars, but the plates are the same than another same car that is perfectly legal. Police would check for suspicious cars to check the car plates, so if the make and model match, it won't raise any alarm.
Over here, if you want to have another plate -say yours was stolen, lost or damaged in a crash- you need to show your title and they make a record to who and when has ordered another plate. I don't know whether those pieces of paper are transcribed to electronic form, and I have sometimes being "trusted" and had plates made without showing title. So I guess it is not that hard to have another plate made. Over here, burglars won't waste their time stealing the plate; they will steal the whole car, commit the crime -or use it till it runs out of gas- and then steal another one.
