Ok, this is a touchy subject and since you mentioned you don't want to share them, you at least acknowledge that fact....lol.
It is illegal to copy your dvd's to a backup, in the United States. To be more specific, it's not illegal to copy your dvd's, it's illegal to bypass copyright protection (which is what you have to do to copy your dvd's).
To recap - Fair use of media allows you to change formats of DVDs etc that you own HOWEVER it is illegal to circumvent copy protection methods. As most DVDs carry this you cant rip them without breaking the law.
If any of your dvd's don't have copyright protection, you can legally copy it. Since you will never find any commercial dvd that doesn't have copyright protection, you'll never be able to do what you want to do.
Hope that's clear as mud...