Is web-presence important for researchers? How important is web-presence to researchers? How does its importance vary by fields? (My interest is STEM, theory in particular)

I noticed that there is a pretty large variation in amount of web-presence even within a single field (I will use theoretical computer science/related math as an example). There seems to be 3 different levels of web-presence:


[High] Very active member of various internet tools (MathOverflow, cstheory, blogs, G+, etc) usually accompanied by a clear homepage with all the [Medium] info.
[Medium] A clear up-to date website that provides a clean bibliography/CV (usually with links to self-hosted pdfs), a repository of course-notes and teaching information, and list of students.
[Low] No personal website (or extremely outdated website).


Increasing your web-presence usually requires effort. Should you invest this effort? Or are you just wasting research time?

If you enjoy being active on the internet (so it is not a cost for you, but maybe a time-sync) is there any danger to having a high web presence?
The short answer, at least in theoretical computer science, is yes.  Especially pre-tenure.
The Coin of the Realm in academia is fame.  Hiring and promotion decisions are based primarily on the perceptions of your impact by leaders in the research community.  Those intellectual leaders must know who you are, they must know what you do, and they must think that what you do is excellent.  This is precisely why it's so important to network, network, network — go to conferences, visit other departments, talk to visitors, ask questions, answer questions, go to lunch, drink beer, play pool/golf/frisbee/Settlers of Catan, race go-karts, exchange business cards, all that stuff.  Having a visible online presence is just another form of networking.
Similarly, if you want to attract good students, they have to know who you are, they have to know what you do, and they have to think what you do is interesting.
Similarly, if your work is not freely and easily accessible on the web, it is much less likely to be cited than freely accessible work of comparable quality.
To give some personal examples, I have good reason to believe that these web pages were a significant factor in my academic job search and even my tenure case, and this stuff definitely helped me get promoted.  I expect that these pages similarly helped Suresh, and these pages similarly helped David.