The most common reason for being blacklisted is because one or more computers on your network has become infected with a mass-mailing virus and is sending out spam.
Check to see which blacklists you are on and also why you are blacklisted by visiting http://www.mxtoolbox.com/blacklists.aspx and click on the link under the reason column to find out why.
If you can – lock down your firewall to block all outbound traffic on TCP port 25 from all computers except your mail server. Most spammers will try to use this post to send mail, so blocking the port will stop most spam immediately.
Check your computers with a tool such as Malwarebytes http://www.malwarebytes.org and download / install their free software and run a basic scan after updating the software online. Remove anything that it finds.
Once you have located and removed any infections on your computers, re-visit the blacklist sites and request de-listing. Some will do this immediately and others will wait a short while. Some sites will ask you to pay for express de-listing – this is up to you, but do make sure you are infection free before paying as you will quickly get listed again if you have not resolved the problem.