jkath....I don't know about whether or not you could put your family tree on it and keep it private.
This is a site I've used to store my information...
PAF v5.2 Registration
...you can set it up to keep it private and you can share your tree with others if you want to. Unfort., even though I backed up my information my computer messed up and I was unable to get back into my information so I had to start re-entering all that information again. After this situation happening to me twice I gave up and refused to use it again. The best way to keep track of your information is through hard copy in my opinion.
Be careful of some of the sites you use and what information you share. Be sure that if you share your information with anyone to stress the you don't wish for them to share your families information with others without your permission.
Hope this helps!
P.S. Remember your research is only as good as your proof. Be sure to keep record of where you obtained the information.