1.) Make sure that your server is indeed blacklisted, and figure out what reasons you were blacklisted. Go here: http://mxtoolbox.com/blacklists.aspx
2.) You should check and see if your server is an open relay, which could be the source of the issue. Go here: http://www.spamhelp.org/shopenrelay/
3.) Go back and check any forms you have on your web pages that send mail out, such as a "contact us" form. You have to be sure you do validation checks (via client or server side scripts) which will prevent these issues. If you do not, then spammers will use your website forms to mail many people, hence why your getting the spam alerts and blacklists.
After all is fixed, request you are removed from the affected blacklist entries via the same site as #1 - http://mxtoolbox.com/blacklists.aspx
I hope this can help you =)