As of April 21st, you can choose the 'Unlisted' setting for your synths when you make them or after they're on the server.
This means that they will not show up:
1) in the search results on the site,
2) on your profile page except to you when you are signed into your account
3) on the global map of Photosynths (if you've geotagged your synths)
However, it is important to know that anyone who you give a synth's link to can visit it even after you mark it "unlisted", so please only give the links of your private synths to people who you trust.
The reason that it is set up this way is so that you can make a private synth, then send the link to your family and they will be able to view it without bothering about signing up for an account on the site, messing about with passwords, or any other nonsense that would discourage them from sharing the experience with you.