Article directories are plenty, but not all equal. Some directories will accept your articles in a blink of an eye, but some won't as they are much pickier about the content they will accept.

If you are new at writing articles you should start with directories such as EzineArticles.com, or GoArticles.com
for example, since they do accept article very easily. If you are a bit more experienced you can post on directories such as Helium.com or AssociatedContent.com and the like, as they are much more demanding on what content they will accept.

In any case you will have to test them for yourself and see what article directories are best for you.

Of course there are other site where you can post your articles such as Squidoo, Hubpages, Wetpaint, Elance, Blogger.com Wordpress and so forth. These are not article directories, there are what we call Web 2.0 or blogs, and do very well on Google Searches, so your articles have a chance to be found and read.