The best width is whatever fits on and makes best use of my screen/window.
Fixed width is a cop-out for designers, putting their convenience over the needs and convenience of their visitors. Ideally, a site will adapt for any screen size, although in realistic terms, you might want to put min-width and max-width constraints on it.
A site that is narrower than my window is wasting space (that assumes people don't have maximised windows on huge screens, because lines over about 20-30 words start to get hard to read), which is no big deal, but is inefficient.
A site that is wider than my screen is a major fail.
Yes, designing for flexible width takes a bit more effort if you're going for a clever layout with lots of positioned elements, but it's almost always possible.
Don't forget that even within a flexible site, you can have fixed width elements, where specific items need to appear at specific sizes.