Mark-k

Many plugins support google authorship integration (less offer google avatar but this is kind of minor feature) so why create another one?
The trick of this plugin is to eliminate the need for copy & pasting the user profile URL\’s, by using the google API to retrieve the required data for the user. An already registered application is used as a proxy for authentication and using the API, and no extra work is involved. For the user, authentication, and gathering the required info, is just one click away from their profile page.
Once authenticated, anyone who can edit the user?s profile can set it to show or hide authorship and use google profile picture as avatar.
Please read the installation instructions, there is more there then the trivial instructions
Network use
The plugin will work for any sub site in the network for which it was activated (or if the plugin is network activated).
Any change the user will make to its profile will impact all the sites in the netwrok in which the user had posted or commented.
Limitations
User still needs to add the site to his G+ profile \?contributor to\? or \?profile\? links in order for the google authorship to work. 
Only the user can authenticate himself, therefor an admin can not set authorship or avatar instead of the user. 
In network usage, sub sites admins can?t edit other users profile therefor they will not have any control and only the super admin will be able to change the settings.

Simple Google Authorship and Avatar

Enables users to easily claim google authorship on their content and use their google profile picture as an avatar

ajitae

Google Plus Plugin for WordPress allows you to Add Google Plus Widgets, Google Api Console required. 
Simple and fast, just paste your google plus profile ID under “GP Dashboard” Option Page after installed.
Google Plus Plugin Features
<ol>
<li>Google Plus Stream</li>
<li>Google Plus Profile</li>
<li>Google Plus One</li>
</ol>

Google Plus

Google Plus Plugin for WordPress allows you to Add Google Plus Widgets, Google Api Console required.

Simple Google Authorship and Avatar vs Google Plus