I own or manage a lot of websites, and checking to see if DMOZ has accepted my submissions is a chore that I often forget to do. I also tend to forget exactly what category I've submitted it to. When you submit a site to DMOZ, make a note of the category. An excel spreadsheet is a good tool to use if you have many websites to track. You will especially need to know the category if you ever have to check the status at www.resource-zone.com.
Before heading to resource zone, however, check to see if your site has been accepted by registering at www.seotie.com. The service is free, and you can set up schedules which keep track of all your submission statuses for all your domain names. I set mine up to check once a week. Then I just log into my account and see if any of them have been accepted.