Precondition: You must enforce users to log in when they book, otherwise the feature won't be available.
To do so, click the cog icon, then select the bookings tab, edit and enable "Booking requires login"

A set of limits can be added to each slot booking type ("tables", "sports courts", "daybeds", "sports gear", "places"), but due to it's nature won't be available for activity and service bookings.

To create a limit, go to the booking type in the left hand navigation and click the "Set limits" button on the top right (the cross sign shows that limits are currently disabled):

Now you can set limits: In this example, each guest can make two bookings at speciality restaurants in total, but can only visit each of the three available restaurants once.

The Timeframe indicates which time span is used to calculate if the guests have reached their limits.

The option "Block bookings when limit is reached" will block the guests from entering the booking form when they try to make another booking.

The option "Allow bookings when limit is reached" will show a warning that the guests will be charged for additional bookings.

This is how guests will see these messages:

Please keep in mind that the limits are set per booking type, e.g. tables. You can create a separate set for other booking types to e.g. limit the amount of bookings users can make for tennis courts.