Well to begin with, NCH offers its own conferencing software called Quorum.
While it doesn't give you as much control over the conference as some other conferencing apps do, it does provide some functionality that is rarely seen in other apps. For example, users can join the conference from a VoIP phone / soft phone, a land-line (assuming you have set-up a VoIP inbound DID number directed to Quorum, and last but not least it's possible to join the conference from any computer with a web browser, headphones, and microphone using an online web interface (and I believe an embedded Java applet).
Quorum also provides an easy to set-up interface (both through the application itself, and through the web interface. It's also easy to set-up with NCH's other software like Express Talk.
Another conferencing app to look into is the Conference module that is part of FreePBX (which runs off the Asterisk PBX). This conferencing app is pretty basic, but it does provide some of the smaller (and useful) features that Quorum doesn't. For example, you can have it announce or play a ping sound when users join and leave the conference. You can also provide users an admins with a menu they can access during the conference that lets them access features such as muting, adjusting volume, blocking users (admins/conference leaders only), and so on.
The conferencing app of FreePBX also has the advantage of being free, which Quorum is not, however it lacks a web interface for people to join the conference on, which seems to be important for your case as you said 'web conference appliance.' Also quorum can run of an existing Windows computer just like any other program, where as Asterisk (with FreePBX) requires a dedicated server (for the most part) running Linux.