I was contacted by a copyright troll after a site I had hosted used a copyrighted image. Annoyingly the site was no longer active, only visible through the holding URL I had set up during the initial development of the site some years before. Google was crawling that site allowing discovery by the troller, and then they got my contact details from WHOIS. They had no legal recourse but they harrassed me for months. I will never ever put my own details in any WHOIS record ever again. Lessons also learnt about holding URLs and disclaimers on 404 pages...
I can't say what is the value for having a private registration, but there is definitely considerable value in not having your own personal contact information available via WHOIS.
Also, everywhere I have ever worked, and personally, I have received through the mail dodgy "renewal" notices that obtained address details through WHOIS records for domains we own. It is definitely abused for both spam and snail junk mail.
It would be pretty interesting to do some kind of audit using honey-trap addresses for both email and physical addresses in WHOIS.