Yes. From your WP admin main menu:
Settings > General > Membership > Check/Uncheck “Anyone can register” Box > Save Changes
Also, see the “New User Default Role” option just below.
In terms of advanced control, there are many great plugins to enhance user registration:
– https://wordpress.org/plugins/theme-my-login/ will white label the user process to be more professional/presentable
– https://wordpress.org/plugins/stop-spammer-registrations-plugin/ will do a great deal to protect your site from fake/spam users
– https://wordpress.org/plugins/members/ to control member roles/access more specifically
And tons of other plugins:
https://wordpress.org/plugins/search.php?q=members
https://wordpress.org/plugins/search.php?q=users