I pride myself in being somewhat of a neo-Luddite when it comes to history. I take notes on paper and tend to print anything I want to read. However, the internet has made a wealth of new knowledge and information available to a much broader audience. As such, more and more research is done online as databases (and especially keyword searching) take much of the traditional drudge work out of research.
That said, the internet is also very fragile and information is constantly disappearing, being moved, or simply updated. This makes it much harder to accurately cite from a web source. In Chicago referencing, the "Accessed on" requirement for web sources helps, but it simply states that the information was available on that date. This very useful article on ActiveHistory.ca shows you how to better preserve web content, cite it more reliably and find information which has disappeared. Definitely worth a read: Three Tools for the Web-Savvy Historian: Memento, Zotero, and WebCite