Even though folks do use machines with higher resolutions, they will often resize the browser window to a smaller size. As I am typing this, I would say my window is only about 60% of my screen size.
I would recommend whatever finished size you make your site to use what is called a liquid layout. A liquid layout is one that when someone makes the browser window smaller than a full screen the website readjusts itself and still shows in it's entirety and retains the layout. If you resize your window to the maximum width of your screen and then slowly make it narrower; you will see what I mean. (Though, it reaches a certain point and stops resizing - but you should get the idea.) If you use Google Adsense, you will lose a bit of your fluidity as their ad blocks don't resize all that much.
That said, if you are going for one of the more graphic-driven modern looking layouts; you can opt to make a site that isn't all things to all people. Just make sure that you make that choice on purpose rather than by oversight.
Since your original question mentioned computers, that also brings up the point of Mac vs PC and the differences in Internet Explorer, Firefox, Safari, and all the other web browsers folks use. I have a PC, I've gotten my best results when I test in Firefox (it adheres better to the standards) and then tweak slightly for Explorer. Since I've started doing it this way, instead of the opposite, I have found I get better results on the Mac as well.
If you have a PC and don't have Firefox installed, I would highly recommend you get it. It is free and can be downloaded from the official site or from Google. As an added bonus, it handles pop-ups and other junk much better than Explorer does.
This topic is one that is frequently discussed on many webmaster forums. The threads are often quite long and sometimes turn somewhat heated.
Another wrinkle is that some folks are now surfing with hand-held devices. My site logs would indicate I've had a few visitors using them. My crafty site doesn't shrink as well as I would like it to mainly because of the Google ads. If you don't plan on using 3rd party content, you may want to test and program to allow folks to make the window quite narrow.
I hope I've been helpful and not just long winded.
The best advice anyone can give you is to consider your target audience and consider the level of computing sophistication they have and whether they would tend to have older or newer machines. And if they know how and are willing to resize the window if your site doesn't fit in what they normally use.