Google Chrome's auto-update feature is the most effective and efficient as it keep your browser update with latest version immediately after every release of the software. Unfortunately, even if Chrome installs the latest version, you can't use it until you restart the browser. Google started to add a small orange dot next to the wrench icon and show messages like: "Old school's not cool. Google Chrome is woefully out of date because it hasn't crashed or restarted in a while. Restart Chrome to apply update."
Gmail's help center lists the supported browsers and includes the minimum version number required next to each browser, except Google Chrome.
[Thanks, Chris Messina, Alex]