I know the standard width of content should be 940px if you want to use all its columns properly. But are there cases where I should use 960px for content? I am just having a dispute with my colleague about what's preferred size - 940px or 960px. As I understand it should be 940px, as it is being used on most sites that use this grid system. So, what's the right width?
You should use the "grid_12" class for a full-width column, even though you already have the "container_12" element. So 940px is the correct size, as seen on the demo page; it lines up the edges of the columns in the same way as a "grid_2" column above two "grid_1" columns.
The right width, for the 960.gs system, is 940px. That's the decision the designer made. The extra horizontal pixels are reserved for side margins to prevent the layout from butting up to the browser chrome.
There's really no "preferred" answer here, as a 960px wide column isn't even an option under this system. (Barring customizations, but then you're not really using 960gs anymore.) If you're using the system, you accept this as part of its design constraints. If you need the layout to work differently, there are other systems, like Blueprint, that don't impose side margins and you can pick one of those instead, or use a grid generator to come up with whatever measurements you want. (Blueprint is actually based on 950px, but you get the idea.)