What are the advantages of installing programs in AppData like Google Chrome?

Windows still lacks a convention for per-user installation.

• When an installer asks whether to install for the current user or all users, it really only refers to shortcut placement (Start Menu; Desktop). The actual application files still go in the system-wide %PROGRAMFILES%.
• Microsoft's own ClickOnce works around this by creating a completely non-standard %USERPROFILE%\Local Settings\Apps (%USERPROFILE%\AppData\Roaming on Vista / Server 2008) directory, with both program files and configuration data in there.

(I'm at a loss why Microsoft couldn't add a per-user Program Files directory in Vista. For example, in OS X, you can create a ~/Applications, and the Finder will give it an appropriate icon. Apps like CrossOver and Adobe AIR automatically use that, defaulting to per-user apps. Thus, no permissions issues.)

What you probably should do: if the user is not an admin, install in the user directory; if they do, give them both options.

One advantage nobody mentioned are silent auto-updates. Chrome has an updater process that runs all the time and immediately updates your chrome installation.

I think their use-case is non-standard. They need a way to fix vulnerability issues (since it's a browser) as soon as possible. Waiting for admins approving every single update company-wide, is simply not good enough.

As far as I can tell, the only reason why Chrome installs into the Application Data folder is so that non-admin users can install it.

The Chrome installer currently does not allow the user to pick where the application is to be installed. Don't do that – instead, give the user a choice between a per-user (somewhere like App Data) and computer-wide (Program Files) installation.