Other than to drink coffee, is the purpose of coffee breaks to build a sense of belonging and collegiality? In an internet era where one can build networks and work on a project with people across the globe, are coffee breaks still important today? To be specific, I am thinking of an academic setting, where it is the norm to network and collaborate with people outside one's own university or department.
If you're not working when your colleague is, or they're on break when you want to ask a question, someone has to wait for however long the break goes for. That's inefficient and annoying, and breaks the flow of work.
If the manager wants to be sure everybody is working the time they should, and getting the breaks they should, it's much easier to see whether someone is over-/underclocking since everybody's break starts and ends together.
It's easy enough to find a quiet corner when you don't want to chat during team breaks, but really hard to find a partner for backgammon when you're going alone. Team breaks mean you're still in a team-based mindset, minimising the interruption to work flow again.
If the head of your department wants you to go for coffee regularly, you go. If it's just colleagues, you should try to go on some sort of regular basis.
This is where you really find out what is going on in your work world. This helps people put a face to a name and treat you more like a person.
Yes you can connect over the Internet, but that should help enrich other relationships or maintain those that are physically distant. It's not a substitute for one on one interaction in person. If you don't feel you do well in person, you can always limit your coffee breaks, but I would recommend using it as an opportunity to improve your inter-personal skills.