It all depends. If you want everyone to know who made your site then don't make the domain private.
If you are doing something that is a little shady or can be flooded with hate mail or phone calls then make it private.
Also, just a tip (if you don't know this already), don't ever use your real legal information when registering your domain. And what I mean by that is, if you're not doing it under a business name; then do not do this ...
My Real Name
My Real Address
My Real City, My Real State + Zip
My Real Phone number
You want get yourself a PO Box and a call forwarding or voicemail service (like Grandcentral.com). And make your registration info like this.
J. Doe (First Initial + Last name)
PO Box 123 (Your real PO Box Info)
NY, NY 11136
1212-111-1111 (Your call forwarding or voicemail #)
That way you could filter who contacts you. If not you might get some crazies calling you at all hours of the night. Or they might just visit your home. Don't laugh, I would call people to buy their domain & their kid pick up the phone. That's not a good thing.