Brian Messenlehner

Display a Google+ Direct Connect Badge on your site via widget or shortcode, allow your members to login/register via their Google+ account or sync your Google+ stream with your blog posts or BuddyPress activity via the Google+ API.
WordPress Google+ Connect allow your website members the ability to register and/or log in via their Google+ account utilizing the Google+ API. Set up a Google Plus Application and store the API credentials in the WordPress backend, when a user clicks on the “Login with Google+” button that gets added to the WP log in screen or anywhere via a short code and authenticates their Google Plus account a WordPress account will be created with their G+ information and they will automatically be logged in. Any existing WordPress users can also log in via Google+ and link their two accounts.
If BuddyPress is enabled a Google+ login button will appear on the sidebar login and the registration page. Google+ profile photos will also be imported in as BuddyPress avatars. Members can stream their Google+ activity into their BuddyPress activity if they choose via the Google+ options screen under the logged in BuddyPress members profile settings page. A cron job runs every 30 minutes to import any new Google plus activity from connected users.
Configure Google+ Direct Connect and help visitors find your Google+ page and add it to their circles from directly within a Google Search.
Configure your Google+ Badge and allow visitors to directly connect with and promote your brand on Google+. Visitors can also add your Google+ page to their circles directly from your website. Badges are easy to configure and can be placed on your website via a short code or a widget.

WP Google Plus Connect

Add Google+ Direct Connect Badge & allow your WordPress/BuddyPress users to register or login via their Google+ account & import their stream  …

H. Peter Pfeufer

Add a sidebarwidget to display the count of your twitterfollowers, your googleplus circles, fans of your facebook-fanpage, and your feedreaders (from feedburner) in your sidebar.
Features
<ul>
<li>Easy install</li>
<li>Panel for easy configuration</li>
<li>No external scripts</li>
<li>Cleaning up database on uninstall</li>
</ul>
Languages
<ul>
<li>German</li>
<li>English</li>
</ul>

WP Google Plus Connect vs Social Impact Widget