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The easy to use free WordPress appointments plugin WP Appointments is packed with lots of innovative features that are rarest to be seen elsewhere. For example, both the front end and back end layouts are based totally on AJAX to give a seamless streamlined user experience. The ease of use goes beyond bounds. It can be used for a great variety of websites, such as doctors, spas, saloons, mechanic, personal trainers, lawyers, cleaning services, and so on. The outlook is high interactive and user friendly.
Features:
<iframe loading="lazy" class="youtube-player" width="750" height="422" src="https://www.youtube.com/embed/u_smM0ObkDU?version=3&rel=1&showsearch=0&showinfo=1&iv_load_policy=1&fs=1&hl=en-US&autohide=2&wmode=transparent" allowfullscreen="true" style="border:0;" sandbox="allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox"></iframe>
<ul>
<li>Totally AJAX-based Frontend & Backend</li>
<li>Interactive design with inspiring graphics</li>
<li>Multipurpose utility </li>
<li>Easy & quick installation</li>
<li>Auto Template Generator included </li>
<li>Email Template Builder </li>
<li>Managements of multiple locations or branches </li>
<li>Management of multiple services</li>
<li>Management of multiple workers</li>
<li>Extremely flexible timetable with time slots management </li>
<li>Fully device optimize layout</li>
<li>Translation support</li>
</ul>
Pro Version:
Pro Version of Wp Appointments is up for sale on CodeCanyon with countless extra features. Pro Version is covering 8 niches and more are on their way. In the pro version you can manage appointments, bookings, locations, services, team members, timetable, payment gateways and users. 
<a href="http://codecanyon.net/item/wpappointments-paid-appointments-system-wp-plugin/14480806" rel="nofollow ugc">Upgrade to Pro Version</a>

Wp Appointments

With totally AJAX based front & back ends, WP Appointments is a fully managed and flexible tool for building powerful appointments systems.

codepeople

CP Appointment Calendar is a WordPress plugin which allows you to define “available” time slots that can be booked by the website visitors. It’s integrated with Paypal for receiving the booking payments.
It’s pretty useful for booking/management of meetings/appointments for lawyers firms, teachers, doctors, veterinaries, beauticians, etc… and for any kind of activity which is developed with specific schedule during the day.
Features:
<ul>
<li>The website visitors can select an available time slot for the appointment and pay for it through Paypal / credit cards.</li>
<li>Once a time slot has been booked and paid it’s doesn’t appear as available in order to prevent duplicated bookings.</li>
<li>You receive an email after each confirmed (paid) booking.</li>
<li>The user receives a thank you/confirmation email after completing the payment.</li>
<li>Allows customizing the contents of the notification/confirmation emails.</li>
<li>Allows defining the product name at Paypal, the currency, the Paypal language and amount to pay for a booking (you can set zero to let the user pay/donate the desired amount).</li>
<li>Allows defining the working days and the exact time slots available.</li>
<li>Allows defining the number of months (calendar pages) to show at the same time for the booking calendar.</li>
<li>Supports date format as mm/dd/yyyy and dd/mm/yyyy</li>
<li>Supports both am/pm and military time.</li>
<li>You can define the start day of the week.</li>
<li>You can define the minimum available date and the maximum available date for the bookings.</li>
<li>You can restrict specific dates.</li>
<li>Easy Ajax administration for the calendar.</li>
</ul>
Please note that this is a plugin originally designed to accept bookings linked to PayPal payments. The feature for working without PayPal is implemented/available in the Pro version: https://wordpress.dwbooster.com/calendars/cp-appointment-calendar#download

CP Appointment Calendar

CP Appointment Calendar allows you to define "available" time slots that can be booked by the website visitors.

Wp Appointments vs CP Appointment Calendar