Google has launched a Chrome extension for the +1 button, so you can easily +1 any piece of content that you come across on the web, regardless of whether it not it has its own button readily available. The description for the extension says:
+1 button is shorthand for "this is pretty cool" or "you should check this out." Now you can +1 the pages you think are worth visiting no matter where you are on the web.
+1's can help your friends, contacts, and others on the web find the best stuff when they search. By installing the +1 extension, you can publicly +1 any page that you're visiting with one easy click.
You can manage your +1’s in a new tab on your Google profile (https://profiles.google.com). You can show your +1’s tab to the world, or keep it private and just use it to personally manage the ever-expanding record of things you love around the web.
***THIS ISN’T THE USUAL YADA YADA!***
By installing this extension, you agree to the Terms of Service at http://chrome.google.com/extensions/intl/en/gallery_tos.html.
The +1 button is not only helpful for telling Google that a piece of content would be good in a set of search results for a relevant query. Thanks to recently added functionality, it also allows you to share content back to your Google+ circles, not unlike Facebook's "like" button and News Feed functionality. In other words, users have more of a reason to click it now. Unfortunately, this Circles-sharing functionality seems to be missing from the extension. Perhaps in an update that will be changed.