You are going to get a million different answers to this question. Everyone has an opinion on whether older, smaller monitors should be supported.
My

:
1. Design to support what YOUR target audience uses.
2. Don't worry about what the W3C browser stats and Browser News stats say, they tend to have a more tech savvy audience than the average website therefore tend to have the latest greatest equipment.
3. Consider how the site will look on mobile devices.
4. Make the design adjust to the user's monitor size. a.k.a. Flexible (Liquid) design.
5. Consider that our society is aging therefore poor vision is a consideration and those people may choose to use 800 x 600 or 1024 x 768 resolution to surf the net.
6. Don't use fixed font size in consideration of those in point #5 and others who prefer lower resolution.