Finding extensions for Joomla 1.5 is not so easy any more, and when you do find something you need there is a good chance it doesn't work anymore (php versions, api changes etc).
I was asked today to add a recaptcha field to the standard contct form on a 1.5 site. Please, no comments about upgrading, it is not my site and not my decision, the job was to add the field, full stop.
It wasn't so hard to find an existing plugin, but if you use recaptcha on an existing site then you are probably aware that Google recently changed the urls to access the service.
UPDATE - V1 recaptcha keys no longer work, so my version of this plugin is useless. You can find a version which has been updated to use V2 keys here: https://github.com/milkycode/joomla_recaptcha_j15
I picked up the plugin from here: https://code.google.com/p/joomla-recaptcha/ and updated the service urls to get it going.
If you have a 1.5 site and would like to add recaptcha to the Joomla contact form, you can download a copy from github: https://github.com/robwent/plg_recaptcha_j15 (DO NOT USE, see the update above)
There are no fancy options to change the theme, but hey, you should be updating your site anyway ;)
You can look through old 1.5 extensions in the archives which are set to be deleted on the 1st March 2014:
http://archive.extensions.joomla.org/ (No longer exists)