One of the elementary things that the Google browser is missing is support for some kind of plugins or extensions system that Firefox has been supporting for a long time. Google announced plans to support an extension API in later builds of the web browser but it currently lacks that support and that could be one of the reasons why many users shy away from the browser. That and the fact that the browser is still looking to the outside like a very early beta build.
One interesting addition to the latest beta builds of the Google Chrome browser is basic userscript support. Since there is no way of adding extensions to Chrome yet users have to live with some limitations. Only scripts in c:\scripts are loaded and only if the user adds the parameter --enable-greasemonkey by appending it to the program's launch shortcut.
There is another serious limitation. The scripts are not limited to a domain but will work on all domains which is usually handled by the @include metadata. The metadata part is ignored which could be problematic when loading some scripts as they will run on all sites and may cause issues or higher than usual memory usage.
Userscript support was added in build 3499 which is available from the Chromium build ftp. Support is also included in later builds including the latest Google Chrome 3601 build.
Update: The Google Chrome web browser has come a long way since its humble beginnings. Google has integrated the extension API into the Chrome browser which, while not as powerful as Firefox's, provides Chrome users with options to install extensions in the web browser.
Greasemonkey support on the other hand is not the right term for what Google has added back in 2008. What the company did add is basic support for so called userscripts. The feature is now integrated fully in Chrome, which means there is no need anymore to enable it with the launch parameter.
Support is basic on the other hand, and Chrome users may want to consider improving it by installing the Tampermonkey extension in the browser. If that is not done, some userscripts won't work in the web browser.
You should also be aware of the fact that Google has implemented a change in Chrome that prevents the direct installation of userscripts in the browser.
In the near future, the company will furthermore block third party extension and script installations from any source in Chrome Stable and Beta versions.