The salt won't protect against poor passwords (common passwords and dictionary words) but it will help relatively good passwords stay secure in the face of ever-expanding collections of rainbow tables. For example there is a 5GB table currently available from freerainbowtables.com that allows you to look up the plain text for any MD5 hash of a string up to 6 characters, including a relatively good password like "F8% z5". Eventually they will expand to 7 characters, then 8... Adding salt makes a rainbow table attack much less practical. I would expect that even a 16-bit random salt would require a rainbow table to be 65,000 times as large.
If you don't want to give your customers a heart attack: add plenty of salt.