I have written an edit counter, because Kate's and Interiot's tools went down with the toolserver changes and Interiot's Tool2 (which is very similar to this one) apparently doesn't work in Internet Explorer.
To install it, follow this link and paste in this text at the end:
importScript('User:Ais523/editcount.js');
To use this tool, go onto a user's Contributions page and click on the 'count' tab the script adds there. Your browser should scan through the users contributions, counting them. If the tab does not appear, try bypassing your cache (on most browsers, hold down Shift and click on your browser's refresh/reload button on any Wikipedia page).