1. How would you define the term blogging?
On occasions like this, I tend to have a look on Wikipedia to see if the multiple users there have come up with a good definition that might nicely encapsulate blogs and blogging, and on this occasion I am not disappointed:
Blogs provide commentary or news on a particular subject, such as food, politics, or local news; some function as more personal online diaries. A typical blog combines text, images, and links to other blogs, web pages, and other media related to its topic. The ability for readers to leave comments in an interactive format is an important part of most early blogs. Most blogs are primarily textual although some focus on photographs (photoblog), sketchblog, videos (vlog), or audio (podcasting), and are part of a wider network of social media.
The term "blog" is a portmanteau, or, in other words, a blend of the words web and log (Web log). "Blog" can also be used as a verb, meaning to maintain or add content to a blog.
I would be foolish to try to improve on that.
2. What blogs-- including academic, institutional, corporate, business, or personal--do you currently participate in?
I am the author of this blog (NT Gateway Weblog), which has been running for three and a half years. It is an academic blog focusing primarily on academic New Testament teaching and research. Although my employer's name appears in the heading, it is not sponsored by my employer and is hosted on my own server. Since it is an academic blog, I try to avoid straying into personal interests, and I try to avoid commenting on issues on which I have no expertise. I do occasionally discuss issues of general interest in higher education since I see those as relevant to the general context of the blog.
I also guest post occasionally (approximately every week or two) on my wife's blog, The Americanization of Emily, which is a more of a personal / family blog in which we reflect on the experience of being a British family living in America. Come to think of it, this provides a useful illustration of the general point. I would never mention this blog in professional academic materials, CV etc., because of its personal, non-academic nature. It is a quite different thing from an academic blog in spite of the fact that it belongs in the same broad genre (blog).
3. How could blogs be utilized in education?
This is a huge question. We are only at the beginnings of seeing how massive blogs will become in education. Imagine someone saying in 1994, "How could the internet be utilized in education?" and that's the kind of stage we are at. Many university teachers are already using blogs successfully in their teaching. An example in our area is Jim Davila at the University of St Andrews who is currently running the Old Testament Pseudepigrapha Blog in association with a course he is teaching. I have not experimented with that yet myself, though I do often blog about topics related to my teaching, and write sketches of things I will be teaching, or write notes and reflections on things I have taught, all of which help to improve the quality of my course offerings -- I hope.
A blog can be hugely helpful in one's research, in developing one's ideas, in engaging directly with others, in disseminating research and so on. I suppose one of the ways in which I find it particularly useful is in the live interaction that blogging generates. When I publish an article, I have to wait months (at least) and years before I receive published responses, and frequently those responses do not engage in detail with the case (you know, a footnote here, a citation there). And by the time that the published reactions to one's published works comes in, one is already working on other things, and one's mind is sometimes elsewhere. I am overstating the point, but I hope you see what I am saying. Academic blogging, on the other hand, allows you to get feedback and to interact while you are at the stage of developing and articulating your ideas, while the topic is fresh, interesting and lively and while you have the energy to pursue it with others. I see this as a major step forward in the academic life, and especially in taking forward the extra mural vision of the best universities and the most conscientious scholars. This is a point I could talk and talk and talk about, and no doubt I will return to it on this blog in the future.
4. Is it possible that online publications such as blogs could be used in developing a new metric in determining tenure for assistant professors and promotion -- which include higher ranks as well-- at university?
This is the question that began my interest in this topic, having read Cathy Davidson's answer. My first answer is here in Should Blogs Count for Tenure? but I hope to comment a little more in due course, partly in response to others who have commented on the question and who are less positive than I about the possibilities. At this point, let me just summarise my thoughts by saying the following: Appointments, Promotions and Tenure Committees, if they are doing their job thoroughly, should be looking at all aspects of a candidate's academic career. If a given candidate has a successful, well respected academic blog, to which s/he had drawn attention in the documentation, that candidate has a right to expect the committee to take it seriously and, if the academic quality is indeed strong, for it to be favourably regarded in the application. I suspect that in years to come we will be surprised that we even found ourselves asking the question, in the same way that now no one would seriously entertain doubts about drawing attention to well constructed academic websites in one's applications for appointments, promotions and tenure.