Look for a privacy seal. 
Check out the company that provides the approval seal.  Check to see if the vendor displaying the seal is actually a member, by clicking on the seal.  To see if a vendor is a VeriSign Secure Site Seal member, search the Secure Site Index.

If no seal, read their privacy policy. If you don't like it, leave.
Look for NoExCorProTerm:

• Notification -- Do they collect information on consumers?,
• Exhibition -- Do they reveal it to others for any purpose?,
• Correlation -- Do they cross-reference it in any way?,
• Correction -- Do they allow consumers to review collected information and make modifications?,
• Protection -- Do they describe how collected information is secured?,
• Termination -- Do they indicate how long information is held, and how it is purged?

If no policy disclosed, go elsewhere.
An FTC study of March 1998, found that only 14% of 1400 websites had privacy policies.  An April 2000 study by enonymous.com checked the 1000 most heavily visited sites, and found that 63% posted some sort of privacy policy.   You be the judge.