Though your state's Department of Motor Vehicles site may require you to enter this information, no other site should
Social Security number
You can't check your credit rating at the sites of Experian, Equifax, and TransUnion without giving this information. No other site (except that of the Social Security Administration itself) should require it.
Very Infrequently Provide Your...
Bank account number
Your bank will probably require this number when it sets up your online banking, as will any credit-card accounts you set up with automatic payments from the bank account. After that, no other sites should ask for or need this information.
Passwords
Only a site you're logging in to should ask for a password. Don't share one with any other site. Also, use a different password for each site, and avoid using real words in your passwords. If the resulting smorgasbord of passwords becomes confusing, use a password manager such as Password Safe.
Somewhat More Often (but Cautiously) Provide Your...
Credit card number
You can't shop online without it, but be careful with sites that you don't know by reputation. If your bank offers temporary or virtual credit card numbers, use them (browse for more on disposable card numbers). Or keep a separate credit card account for purchases at sites you're not comfortable with.
Mother's maiden name
This information could be used, along with other data, to steal your identity, so be careful. Some Web sites ask for this name to confirm release of your password if you forget it, but we recommend that you use other information, such as your high school or your pet's name, for this purpose, when the site allows you to do so.
Home address
As with credit card numbers, you can't entirely avoid sharing your home address when you're making a purchase, but do so only when necessary: Identity thieves find this information quite useful.
Date of birth
If bad guys get hold of this one, you can't change it (no matter how much you might want to). Many sites that ask for your birthdate do so only for marketing purposes, so fudge away. Others ask for it in order to verify your age.