I saw Zuckerberg walking in Palo Alto with wife, child and dog and no security visible just over a year ago. If he has 24/7 security, either they're very discreet or it started recently.
I would bet on them being discreet. Good security is very good at making people unaware that security is present. I recall showing my relatives around the Googleplex when I worked there, having my brother-in-law comment on the seeming lack of security for such a high-value target, and then telling him "No, they're there - if you try to walk off with a laptop or take pictures of something you're not supposed to, they'll come running."
I don't have a link handy, but it has been documented that Zuckerberg outspends all other CEOs on personal safety by a huge margin (something like x10).
Consider that Steve Jobs famously chided his friend Larry Ellison for having 24/7 bodyguards.
http://www.telegraph.co.uk/technology/mark-zuckerberg/121590...
I would bet on them being discreet. Good security is very good at making people unaware that security is present. I recall showing my relatives around the Googleplex when I worked there, having my brother-in-law comment on the seeming lack of security for such a high-value target, and then telling him "No, they're there - if you try to walk off with a laptop or take pictures of something you're not supposed to, they'll come running."