Do third party cookies have common uses other than advertising?

It's possible that you might have issues if you disable third party cookies.

See below:

When viewing a Web page, images or other objects contained within this page may reside on servers besides just the URL shown in your browser.

While rendering the page, the browser downloads all these objects. Most modern websites that you view contain information from lots of different sources. For example, if you type www.domain.com into your browser, widgets and advertisements within this page are often served from a different domain source. While this information is being retrieved, some of these sources may set cookies in your browser.

First-party cookies are cookies that are set by the same domain that is in your browser's address bar. Third-party cookies are cookies being set by one of these widgets or other inserts coming from a different domain.

Source: http://en.wikipedia.org/wiki/HTTP_cookie#Third-party_cookies

In other words, disabling third party cookies might render some web page elements useless, if they are loaded from a "third party", that is, from another site than the page a user is visiting.