You can set a project to allow public submissions. This allows customers to enter cases in FogBugz in that project without logging on. A link will appear on the home page to enter a new case, which provides a barebone case entry form your customers can use:
After submitting a case, they are given a ticket number and a link to track the status of their case:
They can bookmark that link and come back at any time to view the status of that case. Their bookmark includes a generated four-letter password so that their case remains private.
FogBugz will also email the customer a confirmation that the case was received:
This email includes a URL with an eight-letter password that shows the status of this case, as well as any other cases entered using the same email address. Because this eight-letter password is only emailed to the email address the customer typed, and not shown on the web, if the customer knows the eight-letter password, they have effectively proven that they control that email address, so FogBugz lets them see all the cases associated with it.
When a customer looks at a case, they only see their own correspondence. They see the original case as they entered it, and any email back and forth about the case, but they don't see internal assignments, edits, and conversations conducted by logged-on users.