Simple alternative is a WordCount JavaScript bookmark Rated 4 out of 5 stars

The developer has not updated Word Count Plus for a long time so it does not work with Firefox 4 / 5 / 6 etc.
The workaround by Meryl will allow WCP to be installed (as would installing Compatibility Reporter) but the problem is there are serious flaws in it which have not been addressed. For example, the icon was designed to be installed in the Status Bar as it was in 2008 but the Status Bar is now included with the Add-on Bar. This somehow causes the options popup to display with a transparent background and while it works it is really a mess.

For the time-being try this alternative Javascript Bookmark. It is really simple and works brilliantly in Firefox 6.
Go to http://get-business-online.com/blog/internet-marketing/word-count-for-firefox/
Drag the WordCount link to your Bookmarks and you are done.
Select your text and click the link. Displays the number of words and characters.

This user has 2 previous reviews of this add-on.