A cheap, non-acrimonious divorce will probably still cost you about $10k in legal fees. That's not the biggest expense though. I won't get into the details of my specific situation, but I stand to lose about $10k-20k in taxes every year if I get divorced, instead I just split that money with my ex. You definitely have to trust your ex for stuff like this, because being legally married you can get really screwed (she could go crazy on a credit card and I would be liable for half of it).
It doesn't necessarily have to be that expensive. I have a friend who recently went through a very friendly divorce. Both parties had agreed on who would get what. In Washington State there's a process for these types of amicable divorces where a judge doesn't have to make any of these determinations. They had to pay the ~$500 filing fee, wait 90 days and that was it.
I'm sure it varies quite a bit from state to state though.
People I know on the east coast, two couples divorced in two states - same thing, maybe a few hundred in filing fees, that's it. Everyone was in agreement beforehand, judge just made sure the agreements were fair and signed off.