You have to allow for all possibilities. Designing a page specifically so that a typical user won't have to scroll means it could look poor on a large screen. I still tend to prefer relative widths, myself, though I know it's a little old-fashioned. And I realise you are more worried about height than width, but I think the old "don't make the user hit the page down key more than once" rule is completely obsolete, and a short page can look dreadful on a large screen. The BBC is a fairly reliable lead to follow: fixed-width at 974 px, you have to use the scroll button twice with a 1024 monitor, and once even on a 24" Mac.
I also go for around 960px as there is a happy place where it divides down into columns nicely.
I don't worry about the height either - the height of a page should be able to expand to accommodate what ever content is added in the future...not just for the short term.
The argument about the fold on web pages is ongoing & will be for the foreseeable future....it seems to be coming more widely regarded that its not an issue as the general public become more web savvy & understand that they have to scroll down to see more.