In the time it took me to get the reCAPTCHA module installed on the registration page last night, there were 8 bots that registered users. It's now been about 12 hours, and there are no new successful registrations. I did check to make sure that it still works, and it does, so all is well.
I just needed to go to the CAPTCHA admin page, go to the "CAPTCHA points" tab, and enable the user_register_form, then edit it to do a reCAPTCHA. Well, I needed to register the site with google to get keys.
The thing that appealed to me about going with reCAPTCHA instead of one of the other options, is that google will support it and fight the ongoing battle with the spammers, instead of needing to worry about whether the volunteer working on a drupal module has the time to continue the fight at any given time.