Android FOSS repository client (F-Droid is a robot with a passion for Free and Open Source software) provides easy access to a number of interesting FOSS applications.
You can download and install F-Droid application directly from f-droid.org, browse repository online or read reviews.
Hosting your own F-Droid repository
As the project is Open Source you can easily host your own repository.
To do so just grab F-Droid Server source code and follow manual.