Generally speaking, using a grid system is nearly always a good idea: it's simply one of the best available tools to visually organise (i.e. compose) your content in a coherently structured, well-proportioned, yet sufficiently flexible manner. You might want to think of it as best practice. Most good designers regularly use them, unless it makes sense to go for a true freestyle composition approach (in most cases it doesn't, even less on the web and on the desktop – the use of a grid does not need to be obvious at all, BTW). Designing a good grid system that is well suited for a specific purpose and all necessary content requires some training though (at least anybody experienced in typography and similar areas of graphics design should be able to do it).
960gs and the like (e.g. blueprint) on the other hand are ‘just’ good frameworks to simplify technically implementing a working grid system across browsers without re-inventing the wheel each time (heck, that's what frameworks are for :-)) Mind you, you are not forced to use the default 12 or 16 column grid. These settings are, well… just a good default to start from. ;-) But in the end you might want to roll your own. Understanding grid systems comes first though, anyway.
See e.g. http://www.subtraction.com/pics/0703/grids_are_good.pdf and http://www.thegridsystem.org/ for starters. Mark Boulton has a great tutorial on how to design grid systems: http://www.markboulton.co.uk/journal/five-simple-steps-to-designing-grid-systems-part-1