Most registrars offer some sort of ID/Whois protection. Namecheap, who is my preferred registrar, usually gives 1 free year of their Whois Guard service free with each registration.
Whether or not I want my info published depends completely on the name and what I intend to do with it.
When registering your domains do you prefer to have your details private to keep some anonymity? What registrars have this?
I would like a private registration at times but would rather not spend the extra money... I just keep a po box so that my physical address is not available to the world.
I prefer private. It cuts down on spam, both snail mail and e-mail.
In the past, there was someone who registered some domain names using all of my information except (of course) the e-mail. After that, I made all my domain names private.