PluginsPoint

This is an extremely very simple contact form with AJAX which you can use whether in posts or in pages very easily. Using this, site’s admin will get the email. You just need to put the shortcode [kento_contact_form] in any page/post. Email will be sent to admin without page refresh.
Live Preview: http://pluginspoint.com/
<h4>Features</h4>
<ul>
<li>Contact form with ajax.</li>
<li>Shortcode System.</li>
<li>Easy to use and update</li>
</ul>

Kento Ajax Contact Form

Jotform

Feedback buttons are great to get feedback from your website visitors. Since it is easy to send a message to you without leaving the page they will improve the quality and the quantity of the feedback you receive from your visitors.
Feedback button plugin is powered by Jotform. Jotform is the first web based WYSIWYG form builder. Its intuitive drag and drop user interface makes form building a breeze. Using Jotform, you can create forms, integrate them to your site and receive responses by email.
Get feedback from your visitors using Jotform Feedback Button. If you are not aware of the problems on your website you can’t fix them. Feedback button is a great way to help you improve your website.
<h3>External Services</h3>
This plugin connects to external services to provide functionality and improve user experience. Below are the details of the external services used:
Jotform Feedback Button 
 – <a href="https://www.jotform.com/privacy/?utm_source=wordpress&utm_medium=plugin_directory&utm_campaign=feedback_button_plugin_content&utm_content=privacy" rel="nofollow ugc">Privacy Policy</a> 
 – <a href="https://www.jotform.com/terms/?utm_source=wordpress&utm_medium=plugin_directory&utm_campaign=feedback_button_plugin_content&utm_content=terms" rel="nofollow ugc">Terms of Use</a>
Service usage 
– The plugin makes external requests on the following domain to render feedback form functionalities: 
 https://www.jotform.com 
– The plugin uses the domain [https://www.jotform.com] as a service to deliver and render the feedback form.
Asset usage 
– The plugin makes external asset requests on the following domain to enable feedback button functionalities: 
 https://js.jotform.com 
– The plugin uses the domain [https://js.jotform.com] as a asset service to deliver and render the embedded feedback button.

Feedback Button – Jotform

Display a beautiful feedback button on the side of your blog. When a reader clicks on it a feedback form pops up. Completely customizable.

Kento Ajax Contact Form vs Feedback Button – Jotform