The web interface of Android Marketplace lets you remotely install apps to your phones running Android OS. The Android apps in .apk format are then pushed to Android phone Over The Air (OTA) and gets installed in the background automatically. While this happens without you having to play manually with .apk apps, there might be a situation that demands the availability of .apk installation. It can be when you want to have .apk file of the app for which you have already paid for but incompatible with some of your phones or to have a copy of the app that is not available in a particular region. Also what if you don’t have an active internet connection on your phone. Then downloading .apk file on to your desktop and installing it via data cable is the only option. Here is a Chrome extension that lets you download Android apps on to your desktop.
APK Downloader is a Google Chrome extension that allows you to download Android APK files from Marketplace to your computer. After installing this extension and few setup process you will have the option to download free apps from web version of Android Marketplace. The downloaded .apk files can then be transferred to your Android phone and installed. But like what I mentioned it requires you to input few parameters before you can start using it to download apps.
APK Downloader extension require you to disable SSL error warnings, find and input Android Device ID along with Google account details first. Once you input all these and grant access to your Google account then downloading .apk apps is just a matter few seconds. All you have to do is head over to the Android app page and then hit APK Downloader icon on address bar. The step by step procedure can be found here [link].
Note that you need to be on the latest version of Google Chrome 17 and disable SSL error warnings. Only then this extension would work properly.