Chromium (Google Chrome)
Chromium Web Browser
Chromium is the open-source project on which Google Chrome is based.
Take a look at the project.
Windows Version
If it's the Windows version you're after, then read no more, download and install it from Google.
It will keep itself up to date.
Linux Version
If you want this web browser on a Linux machine, then, you can either:
Download the source code and compile it.
Find an already compiled package for your system, download and install it.
Set up a repository, so you can keep it up to date without any fuss.
Building from Source Code
Get the source code (read these instructions).
Compile it (read these instructions).
Download and Install
Setting up a Repository
As root (using su or by any other means):
cd /etc/yum.repos.d/
wget http://repos.fedorapeople.org/repos/spot/chromium/fedora-chromium.repo
yum install chromium