This is one of the classic questions that comes up time and time again in article marketing.
In fact, after Google completed their Panda update that essentially penalized and destroyed content farms, this question comes up even more.
Here's the bottom line...
There's absolutely no benefit at all to submitting your same article to multiple directories, but there is 1 exception.
Let me explain...
If you write one original and unique article, but you submit it to 100 different article directories, Google is only going to display the article 1 time in the search results.
It makes absolutely no sense for Google to display the same article 10 times on the first page of the search results.
That doesn't help Google nor does it help Google's customers.
Plus, you should ask yourself why you're writing the article in the first place.
Is it for search engine rankings or is it for human consumption? It should be for human consumption.
If you are building a business based on search engine rankings, you are playing with fire.
Google can change the algorithm and put you out of business the next day, just like it did with for a lot of people with the infamous Panda update.
Getting search engine rankings is just a benefit of the process, and that's it.
Consequently, that's the exception to the question of this article.
If you have an article that is a high performing article and it's not at the top of page 1, but maybe it's close, then you can write another similar article and submit it to other article directories.
The purpose would be to get that high performing article to the top spot for a particular keyword phrase.
The strategy here is to link to the article you want to move up.
Instead of using the resource box to link to your website, link to the article you want to improve.
Usually you can increase the rankings of that article with this one little strategy.
Other than that, there's no reason to submit the same article to multiple article directories.