We are programming a web application (not \'just\' a web site, but functionality-wise a real application), and have the following discussion for the next release:
Replacing the browser right-click context menu for specific areas of your GUI from your web application can be quite useful. Doing this just to disable the context menu will annoy your users, who may try to find a way around it. Also, removing or replacing the browser right-click context menu from the entire area of your application will usually be annoying and can make it more difficult to debug.
Unfortunately, I cannot offer any more solid arguments, and I'm not exactly taking either side of the argument, but I thought I would share my experience both as a developer of a web application and as a web user.