You cant submit a single article article to many directories because in this case the article will be considered as a duplicate content. What you can do is spin the article. Spinning imparts slight variation to a article and at the same time helps you get rid of the copyright infringement offense.
If the article appears on one site you can submit it to as many directories or search engines as you wish. Takes a bit of work but that's the best way to present it to drive traffic to the originating site. If you submit the same article in full to different sites you are creating diluted content (not duplicate).
If you have the same article under different pages on your site that is duplicate content.
From what I've read duplicate content is not penalized as heavily as it was in Google. Having duplicate content in your archives section for example is not that big a deal anymore, but it still doesn't hurt to noindex it.
One of the reasons for this may be that it is easy to penalize the competition by duplicating their content all over the web...
There are a couple of more established article directories that check more closely for duplicate content submissions so submit the article to them first. I think ezinearticles is one. #*$! forum has lots of info on this promo technique.