If downloading apps from Google Play is too mainstream, you can now use an open source application store like F-Droid. It's an alternative to Google's app store where you'll only find applications with a free license. Thus, all the apps will be free and their source code accessible and editable.
How it works
All open source apps in the same place.
How F-Droid works is very simple. It incorporates three tabs: one for the applications available, another for those that are already installed and a last tab for outstanding updates. After finding the app we're interested in, we'll be able to install it on our Android or access its source code. We can also view the license of each application and information about the latter.
With F-Droid you'll have at your disposal all the open source applications available for Android.