You can include a Profile in your Contribution Pages and Events and include recaptcha for it.
To set up your reCAPTCHA keys visit Administer > System Settings > Misc (/civicrm/admin/setting/misc?reset=1)
Then to set it in your Profile visit
Administer -> Customise Data and Screens -> Profiles
Click on settings link for the profile added on your ...
OK, I found the problem and it was my idiocy. I was trying to get it to show as a logged in user, and it was not. When I went as an anonymous user, it shows up just fine. It totally makes sense, just was not immediately obvious to me.
Looks like a bug- see comments
2 possible workrounds
1) Limit to single participant registration
2) Create new profile w/o captcha and use this as profile for additional participants
Or as you suggest disable captcha for profile entirely
I was able to apply these patches directly to CiviCRM 4.5.4. Looking at the code, this version is virtually identical in the ReCAPTCHA code, so it should work fine (although you may need to manually apply the patches).
Update this file:
First of all, you should really customize CiviCRM by developing extensions. There is a developer guide that will explain you how this is done: https://docs.civicrm.org/dev/en/latest/
If you do want to override anyway, you should first of all navigate to Administer>System Settings>Directories to provide the path to the PHP files, have you done this? If you ...