I see a lot of people saying "Office looks great but I bet it will take a beefy machine to run it". So to tell you what I think:
First, Windows Vista is not required to run Office 2007 (although it is much nicer on it). You need Windows XP sp2 and above. The general specification required to run office is listed as 256Mb RAM and, depending on which version of Office 2007 you are using, 1.5-3Gb of disk space.
The hardware spec on our website says a few other interesting things, in small print at the end of this list has some of the exceptions:
OK so putting all that together, it will install on 256Mb RAM but I think you can see that for it all to work, you probably should think about 512Mb or you won't really get the Outlook Search stuff (a pretty important feature) and if you can stretch to 1Gb, everything starts to work, including the grammar checker.
Asking around the team, Chris Adams (sits next to me) tells me he has it running on a machine with pentium4 512Mb RAM no problem. He also has it on a mobile processor 2 GHz, 1Gb RAM which showed no problem running vista as well.
The weediest machine I've tried it on was my Toshiba P3500 which is a pentium III - M, 1.33GHz with 512Mb RAM. It works OK on that but it does seem to run better if you have more RAM.
So in summary, the spec on the box is not hopelessly optimistic. It is more memory sensitive than processor on most machines and will run fine on 512Mb but if you can get 1Gb, that will definately help.