That's a loaded question, and the true answer depends on the audience. We could design web pages that look somewhat good on 16-color monitors. It is possible. There are JavaScript image replacement options to solve some of the problems of color compatibility, but they are rarely used. But even this approach falls apart when GIF images and JPEG images occur on the same page, as is sometimes necessary.
Monitor resolution is another touchy problem.
Some even go as low as even 640 x 480. Most probably do no realize that, if font size is their concern, this can be adjusted from the browser preferences. Another group has gotten adjusted to whatever settings were present when they bought their system, and not explored further. As if vertical scrolling were not bad enough, horizontal scrolling means that the viewer must sometimes go back and forth for every line of text. It increases the feeling of being stuck in a tunnel.