The Norwegian system is actually much cheaper than the American system when you account for lower recidivism rates and reduced prison sentences.
At least in Sweden, the outcome of being sentenced (losing your job, making it very hard to find a new one) is factored into the sentence (that is, they decrease the prison sentence due to these factors as more punishment will be had after release).
In practice, though... At least it's automatically erased after (IIRC) five years, depending on severity.