Developer redphx has released a Chrome extension that lets you download Android app files (.APK) directly onto your desktop. It hasn't been impossible for Android users to get the files onto their computers before, but the new extension, called APK Downloader, makes it simple.
Why would you want to have the installation files for an Android app on your desktop and not your phone? Well, as seasoned Android users know, not all apps are available on all devices: you can't find and download tablet apps for your phone, for example, and some apps are region locked. However, all apps are visible on the Android Market website, so with this extension you can easily download any app and then sideload it — something that's especially helpful for Android devices that don't have the Android Market, like the Nook Tablet and Kindle Fire.
The extension's compatibile with Windows, OS X, and Linux, and when we tested the extension on a Windows 7 PC everything worked as advertised. It requires Chrome 17 or greater, and once you install the extension you need to make a quick change to your browser shortcut properties to disable SSL error warnings. Once you do that, you give the extension your Google account credentials (the developer invites you to check the source code to see that he isn't collecting this information) and some information from your phone and then you're good to go.
Update: The developer has removed the download link from his site after hearing that users might be able to download paid apps for free using the extension.
Update 2: The extension is now available for download again. The developer updated the extension to version 1.2, removing the ability to download paid apps.