APK Android application package file is the file format used to install onto the Google's Android Operating System. If your are unable find any application in the Android Market Place, using Google you can find free games, Applications, Wallpapers, Widgets etc. You can download apk file using Google search to install in your Android Device.
To Download apk Search Google as follows
index of apk
index of apk games
index of apk skype
parent directory apk
You can search a specific web site for apk, like below
site:mediafire.com apk youtube
site:mediafire.com apk live wallpaper
These are the example how you can get a better result in google search and download the file. You can change the search query as per your application name such as if you want to download Talking Tom Cat for your device then search like this site:mediafire.com apk tomcat.
I think it may be helpful for all Android users to download their applications free using Google.