I noticed the that many site only offer two social login options:
Grooveshark: Google, Twitter
Quora: Facebook, Twitter
Digg:: Facebook, Twitter
How does this improve the user experience?
At Stack Exchange, we have so many login options, that we made the decision to only show some of them initially and then hide the rest behind the more options link.
Too many options just confuses users who don't understand what open ID is or how they could log into one website with another one.
We chose our options to cover the vast majority of use cases, and here's the data we used. This is sign-ups:
Giving users too many choices is often a bad thing. They're easily overwhelmed and it doesn't take much for them to leave and go to a competitor's site. Also, if you're offered too many options to sign in, you may forget which one you used and have trouble logging in when you revisit the site.
It probably varies from site to site, but I imagine that many companies have done split testing on their users and found that offering only two social logins works best.
Asking how to "improve the user experience" is a fairly nebulous question that encompasses a number of separate elements.
I thought you were wrong on this question with only two social network login - so I made my own very small test and found the following:
Stackexchange at least 4 social login options
Screenr 4 social login options
But Pintrest, Hopflow and Slideshare all uses 2 social login options:
The reason for only using two different social login options are most likely a combination of the likelyhood of a user not having one of two different social login and developer effort. If you have Facebook login as one (and most of the mentioned does) you're probably safe. There are a number of user who doesn't use Facebook, but for a reason. If you don't have Facebook - you're unlikely to have any other social network, and these users would have to login to the site using regular username/password anyway. More isn't always "more".
The second reason is probably implementation that can be very hard, without any real benefit since most users probably have one of the two options. There is also always the posibility to login using the sites own security system. It's always better to implement two login options well, than five bad.