I have a very public web presence from this blog and my web site. I enjoy sharing information and communicating with people via email and occasionally (with a heads-up email first) talking on the telephone. I also spend an hour a week giving free advice to students on their projects, employment hints, and to a more limited degree give feedback on technical ideas. I can enjoy doing this because email is asynchronous: I can handle these interactions when they don't interfere with my work or research.
In the past I have accepted connections on LinkedIn and Facebook from people who I don't know, just t be friendly. However, there is a cost to this.
LinkedIn frequently sends out email statuses of what colleagues (current and present) are doing. I like this for people I know well either personally or through years of email interactions. However, status updates from people I am not closely associated with take time even to ignore.
The situation is worse on Facebook. I used to always accept friend connections from anyone who looked like they were a computer scientist from their public profile (in addition to people I know).
I am a native English speaker with reading knowledge of French. One of the great things about the web is communicating with people from around the world with similar interests. Due to my limited natural language skills however, this has to be in English. Sometimes half of the updates on my Facebook are in languages I can't read.
I am leaving all of my LinkedIn connections as-is but in the last few weeks I have been removing friend connections on Facebook except for close friends, family, and people I have worked with in the past. Checking my Facebook page a few times a week is much more enjoyable.
For other communication, email is best.