I introduced recaptcha to the login screen of a system.

My goal was all about security things like dictionary/bots attacks or other thing of that type.

The users now hate it, Some did not even understand it  and I had to remove it.

When I look around, I don't see many systems with that on the login screen, most of the times on other forms like contact us or sometimes like in stack exchange when you want to post.

It made me wonder is it a good idea to have it on the login screen? 

The way I've seen some large systems do it is to only require a captcha after sequential failed login attempts (ie: reset the count after a valid login).  If you are worried about automated cracking, you could put the captcha at some high number of failures like 20, 50, 100 failed attempts.  Almost no legitimate user will see the captcha, but an automated attack will get hit by it.  

Is it worth it to add this complexity?  Security and UX are trade-offs.  You need to find the correct trade-off for your risk profile. 
