Never post your last name publicly. And, unless there is a legitimate reason, there really isn't any need to do this privately either.
As with your last name, you should never post your address or phone number. If you plan on buying/selling something with another member, be sure you can trust that person before giving out your address or phone number.

The location field in your profile should not contain your city/town. A state or something equivalent is sufficient.

You are typically safe posting your first name online if no other information is posted.

Sensitive information such as social security numbers and credit card numbers should never be posted online.
These should only be submitted through secure forms on company websites you trust.
For example, a government website or your bank's website are usually safe.
Third party website that are well-known, secure, and trusted like eBay, Paypal, Amazon, etc. are also safe. As with other information, this information should not be made public and should only be entered into secure forms.

You know a website is secure if its URL begins with https instead of just http.

You should never agree to meet someone in person unless you know that person.
If you do meet someone from online, make sure you meet them in a public place.
Never meet someone at their house or a place that is not well-populated.

If you're under 13, you should not post any of your information online, whether the website is secure or not.