If you want to keep your family history private then do not put it on the Internet.
If you want it make your data semi-public then there are vaious websites that have restricted access to your data.
Genes Reunited - you only give access to those people who you want to share your tree with.
Tribal Pages - are password protected and you only give your password to those you trust.
I've on mentioned a couple of sites, but there are many others out there that offer a degree of protection and security.
Most sites also offer a 'protect the living' feature which prevents the display of information of people that are less than 100 years old.