Social logins manager Janrain has been tracking the popularity of brand-specific logins via their platform for a couple of years, and have released their data from the last quarter of 2013.
The trend over time can be seen above, and shows Facebook maintaining their dominance across websites. This is not surprising giving that they remain one of the most popular sites on the Internet - and as first movers in the space, they saw rapid uptake of their unified login across the Web.
While Facebook was able to reverse a year-long slide in logins, Google has gained ground in the final quarter of 2013. Here's the overall picture:
Google's gains are impressive, especially given that their social media products have only recently been gaining traction. The transition to Google+ comments on YouTube is likely leading much of this trend; as people get used to having to use their Google ID to login to the many Google products, they will be more open to using it on other sites as well.
Also, given that Google has moved the center of their brand experience via Google+, consumers are much more tied to their Google logins.
Apart from some predictable trends, such as the popularity of LinkedIn for B2B sites with a professional focus, one of the most striking divergences occurred in the retail website sector:
For travel websites, the consideration here must be the utility for both the user and the website. To offer something convenient is vital, as eliminating friction to signup is now expected by consumers.
However, the company must also consider the social sharing benefits they received from certain logins - and oftentimes that means that Facebook is the most vital, given the ability to encourage users to simply share information with their social networks.