They serve a few purposes - I'll try and illustrate from various points of view.
* As a site operator, particularly if you're keen on 'organic' and free traffic, you need to keep on top of the latest in search engine and social marketing. Facebook and other social networks are becoming more important as traffic sources, as 'recommendations' from friends become more trusted. Bing and Facebook reached a deal to prioritize some results based on social recommendations ('likes'), and Google is rolling their own solution, so site owners have incentives to include the links.
* As a user, you generally want to see the most trusted results you can, and occasionally may want to recommend sites to your friends. Facebook's verbs 'like' and 'share' work well here - Google's '+1' is a little more opaque to most web users I'd suspect, but they're trying to convey the same intention.
* As Google/Facebook, you want as much data as possible about the behaviour of web traffic - search, engagement/interaction, conversion rates, even raw traffic figures. Even if people aren't interacting with these widgets, they are still often served up by AJAX from the source. This implies that Google/Facebook/etc see an incoming HTTP request, and sometimes associated cookies/referers. Add a little GeoIP and other user analysis, and you have very valuable data on aggregate.
All these generally seem like 'wins' for the parties involved - and that's usually the sign of good business taking place. For me, the main concern is that all this data belongs not to the general public, but to the widget providers, and large information disparities in any situation can be abused.