The implementation from jhawkwood is for 1.0.x series. To use reCaptcha (
http://recaptcha.net/), requires setting up an account with them. It also looks like you need to set up your public and private keys and add a php file to your Joomla install. You might also ask at (
http://joomlacode.org/gf/project/recaptcha/) for a registration component version that works with your version of Joomla. Start there, get that working, then try the two file mods for the contact form that jhawkwood posted.
I have not tried any of this to see if it works as I don't use the Joomla contact form, instead I use a rather old mosDirectory ( probably a security risk by now) component for contacts. I still had to modify that to add a captcha and require all fields to be filled out (thanks Mr. security minded developer for not doing this in the first place).
Maybe you can allow only registered users to use the contact form, and require those users when registering to click on the link sent by email activating their account. This might cut down some on spam.
*** Not sure why the Joomla developers were/are so pig headed on adding a captcha component to Joomla. Debates on how effective it actually is or isn't aside, it seems many Joomla users would like to see this built in to Joomla to help protect both the contact form and the registration form, so why not offer it built in? There is open source code on sourceforge that I'm sure could be integrated into Joomla fairly easily by a developer. Why not also enable administrators to set some or all form fields as required. My experience with the bots was they only looked to fill the message box. ***