I've seen many people around who want to get in the big ODP mostly because ODP can bring more than a few backlinks (I know there are also other reasons but I want to discuss about this one only). Ok, I came across these websites/directories that uses the ODP data, let's say you submit to all these directories, so when you'll finally get listed in DMOZ it'll not bring you as much backlinks as expected since you're already listed in almost all directories that uses it's database.
Sites listed in that category need to have attribution to ODP which includes a link to submit sites. These submissions go to dmoz.org, and not to the clone. 'Submitting' to all of the clones would be a bad idea.
One caveat to what ishfish said. In a few of the sites listed in that category, there are two options for suggesting/submitting sites. (1) Using the attribution and suggesting the site to the ODP and (2) a submission form that is for that directory alone. One example of that is http://www.magic-directory.com/ - (it just happens to be the first site I looked at last night when I was thinking about commenting on the OPs statement). Notice, once you enter the directory, that at the bottom of the page is the attribution which allows you to suggest a site to the ODP. While at the top of the page is "submit new link" which does not suggest the site to the ODP.
Yes that's exactly what I was saying, you can submit to these directories (their own database) not ODP. What if you are already listed on all these directories and then later on get listed in DMOZ will it create double backlinks from these directories?