tharkun's answer is sort of correct but I just wanted to post a "more correct" answer for anyone else who finds this question in the future.
For some reason, Eclipse needs administrator privileges in Windows 7 and Windows Vista machines. To do this one time, right-click the Eclipse executable or shortcut and click "Run as administrator"; to make it permanent, go to properties, the compatibility tab, and check the "Run this program as an administrator" box.
Despite tharkun's post, perhaps he forgot, Eclipse doesn't have an installer; you simply unzip it. There is no reinstallation necessary. If you run Eclipse normally and find something wrong, and just discovered this answer, you can safely run Eclipse as administrator from now on and nothing will be broken as a result of you not having run as administrator up until this point.
The problems with Eclipse that require administrator mode do not show up immediately, but for example if you check for updates with Eclipse running in non-administrator mode, Eclipse will claim that there are no update sites available. Also some GUI features will have problems.
These problems are likely caused by some of the advanced UAC features meant to protect your system, such as UAC Virtualization. Eclipse can (and hopefully will) be fixed to write only to user space and "play nice" with other Windows applications, but for now we have to simply run it as administrator and trust that it's not taking advantage of the added privileges.
As a sidenote, I just spent several hours trying to figure out how to get Eclipse to write inside the %AppData% directory, in hopes that it would solve this problem and allow Eclipse to be run in user mode, but I could not get Eclipse to honor anything I tried. Oh well...