Just to extend upon eykanal's reply, I'll add a public relations spin to this topic.
IMHO, all depends on the mode in which you operate. If you are an established professor, your website is going to look differently from somebody who is striving to climb the ladder. This also depends slightly on the community you operate in, I'll speak for CS/AI, specifically more applied streams.
As an established member of the community, you rule your time and do not need yourself to be "discovered". Hence you do not need much bragging on your site and can stick to practical info. In the case you are climbing the ladder, your website is your shop-window. You need to have it up for your potential future employers, potential future collaborators, etc. It's can be used as a personal PR shop window. In that case you might want to break down your CV into pieces and include projects you work(ed) on and their descriptions, possibly even attach publications to these entries to document the rate/quality of the deliverables. Many people list Activities section, where they keep a list of academic services they perform, i.e., program/organizing/steering/... committee memberships, refereeing for journals and announcements of edited books, etc. As eykanal pointed out, expanding on teaching activities is important. Now, first and foremost, you want to serve your students, but remember also the (future) hiring committees. They want to see indications of those activities as well.
All in all, anything what can help you in the future, but still won't look as too much bragging about your achievements can be useful, but think about balancing it with practical stuff as well. For example, to add a "human" touch to their academic personas, many people also include "family" section with a handful of links and pictures of their family, pets, hobbies, etc.