I'm sure I'm going to get in trouble with the CNET IT team for this, but I just set up my computer to run Spiceworks, a business network scanning and monitoring application. Spiceworks scans a PC's local network and reports on the health of various items. You can tell which printers are running out of ink, which PCs have out-of-date virus scanners, and so on.
To monitor PCs, you need to be a systems administrator with a network administrator login for the computers in your office. I don't have that access, but I was able to peer into the data the system returned on my own PC, as well as on printers and a few open-access computers here in the office. I found the level of information both deep and clearly presented. For example, administrators with this tool will easily be able to see which applications are installed at the company and which users are running old versions. It can also kick off Windows remote control sessions for hands-on tech support.
Spiceworks also has a full help-desk system through which users can submit service requests. The system then lets you assign and track tickets until they are done.
I confess that Spiceworks isn't wholly Webware: It's software that must be installed on a PC and which runs in the background (download link). It does not, however, require that the monitored PCs run any software aside from the built-in administrative processes that run in Windows by default. One Web angle is that the user interface is browser-based. So the administrator can run the management console from any network-connected PC that can reach the monitoring station.
What's most Webware-ish about this product is its cost: It's free. Web-served ads run on the administrators' interface. I found them unobtrusive. Making money from management software like this via advertising is certainly an interesting (that is to say, highly risky) business model. But if you're trying to run an office full of computers, you could do far worse than this easy-to-use, yet still comprehensive, system and network management product.
Spiceworks will be presenting at the Office 2.0 Conference next week.