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.
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)