Cross broswer compliance.
This is a topic that surprisingly few designers and developers have paid attention to in the past, but that more are starting to pay attention to since the rise of Firefox and also the increasing market share that Apple is gaining in the PC market (and thus an increase in the number of Safari users).
When designing pages, it is important to test in as many browsers, versions, and platforms as possible. Not only do the different browsers show things differently sometimes, but the same browser on different platforms (OS X, Windows, Linux) can be different. Embedded Flash with a transparent background does not work on Linux, for example, while it does on Windows and OS X. One other thing to take into consideration is the fonts available to users on different platforms. Sometimes a site will look drastically different if a different font is used for the text. Remember that the font size also helps determine how wide the text will be, and this can mess up many designs.
One also has to take into consideration the different versions of the browsers that are being used. Internet Explorer 6 on Windows 2000 and earlier behaves differently than version 6 on Windows XP, as a side note. Version 7 is a drastic change from version 6. There are even some fairly major changes from Firefox 1.5 to 2.0. Safari is a rapidly developing browser, and hence it can be financially difficult to test for older versions due to Apple's licensing agreements. I have not personally noted any large differences in the versions of Opera since 7, the only thing that I can think of would be the addition of the opacity CSS statement a relatively short while ago.
The biggest problem with running older versions of browsers is that it is often difficult or impossible to get them to run concurrently on the same operating system. It's often useful to have multiple machines set up with different configurations in order to test as much as possible.