Dropbox does a wonderful job with its right-click functionality.
Hovering with your mouse over a directory looks like this:
Clicking on the underlined link (music) navigates there, but clicking anywhere else in the frame, as well as the "dropdown" sign, or right-clicking(!) opens the following menu:
This has so many benefits:
It doesn't block the user from right-clicking - it gives the users what they wanted (a context menu) and shows them where it can be accessed without a right-click.
This menu is discoverable, unlike the right-click which has to be guessed.
With the onset of touch-based platforms, there's no such thing as a context menu. If you expect your UI to be accessed by touch devices, avoid using them.
Accessibility concerns are relevant if you consider that using a mouse with two buttons is potentially difficult for some people, who may choose a single button mouse or even a different input device than a mouse (such as voice controlled browsers). Although these browsers generally include options to access context menus, it's probably much less likely that users will think to use them to discover additional functionality in a website or app.
On the other hand, Jakob Nielsen reported in 2007 that right click menus are a good convention and users have come to expect them to exist. He doesn't comment on web sites specifically, though, and I would take that into account when considering using them.
Web sites and web apps are two different things. Consider that a web app like Google Docs will have a higher expectability associated with context menus by users than a web site like Amazon.com. Web apps look more like traditional desktop apps and it's therefore not unreasonable for users to expect them to work similarly. Web sites have a different model to conform to.
Whatever you do, it's important to consider what users will expect and design accordingly. A hidden menu like context menus won't help anyone if no one thinks to right click in the first place.