Aaron D. Campbell

This plugins gives you a great framework to use for integrating with MailChimp.
Requires PHP5.

MailChimp Framework

MailChimp integration framework and admin interface as well as WebHook listener.  Requires PHP5.

Danny van Kooten

ibericode

<h4>Newsletter Sign-Up</h4>
<blockquote>
This plugin is in maintenance mode, meaning we no longer develop new features or actively support it. Sorry.
</blockquote>
This plugin adds various sign-up methods to your WordPress website, like sign-up checkboxes in your comment form and a sign-up form to show in posts, pages or widget areas.
<blockquote>
Mailchimp user?
Use <a href="https://wordpress.org/plugins/mailchimp-for-wp/">Mailchimp for WordPress</a> instead. It’s free & so much better.
</blockquote>
This plugin works with almost all third-party email marketing services including Mailchimp, CampaignMonitor, ConstantContact, YMLP, Aweber, iContact, PHPList and Feedblitz. With the right configuration settings, you can make this plugin work with any newsletter service around.
Features:
<ul>
<li>Add a “sign-up to our newsletter” checkbox to your comment form or registration form</li>
<li>Easy customizable Newsletter Sign-Up Form Widget</li>
<li>Embed a sign-up form in your posts with a simple shortcode <code>[nsu_form]</code>.</li>
<li>Embed a sign-up form in your template files by calling <code>nsu_form();</code></li>
<li>Use the Mailchimp or YMLP API or any other third-party newsletter service.</li>
<li>Works with most major mailinglist services like Aweber, Constant Contact, iContact, etc.</li>
<li>Compatible with BuddyPress, MultiSite and bbPress.</li>
</ul>
More information
<ul>
<li><a href="https://mc4wp.com/" rel="nofollow ugc">Mailchimp for WordPress plugin</a></li>
<li>More <a href="https://dannyvankooten.com/wordpress-plugins/" rel="nofollow ugc">WordPress plugins</a> by ibericode</li>
</ul>
<h4>Sign-up checkboxes</h4>
Most of your commenters will be interested in your newsletter as well. This plugin makes it extremely easie for them to subscribe to your mailinglist. With the sign-up checkbox, all they have to do is check it and the plugin will subscribe them to your mailinglist.
You can also add the sign-up checkbox to your WP registration form, your BuddyPress registration form, your MultiSite sign-up forms or your bbPress new topic and new reply forms.
<h4>Sign-up forms</h4>
Easily configure a sign-up form and show it in various places on your website using the sign-up form widget, the <code>[nsu_form]</code> shortcode or the <code>nsu_form()</code> template function.
You can set your own messages and even choose to redirect the visitor to a certain page after signing-up.

Newsletter Sign-Up

Integrate your WordPress site with 3rd-party newsletter services like Aweber and YMLP. Adds various sign-up methods to your site.

MailChimp Framework vs Newsletter Sign-Up