Google Play isn’t the only marketplace for Android apps, here a list of best alternatives to find applications and games released by developers.
In order to enable third party App installation you must enable “Unknown Sources” under Security options of Settings app.
Amazon App Store
It comes next to Google Play store in terms of popularity. There is no web interface for it and you need to download the apk for using it. The apps are categorized into different sections, there are both free and paid apps. Amazon offers one paid app for free each day.
APKMirror (link)
It allows to download the latest releases of Android apps. It hasn’t an official app (to download you need to visit the official website). You won’t find any paid apps on this store though.
GetJar (link)
If you ever owned a J2ME or Symbian based device GetJar doesn’t sounds new. There’s an official app for GetJar but you can also use it through the web interface. The site is well organized and categorized, but the apps may not always be up to date.
AppBrain (link)
In this marketplace you can find paid apps free for a limited time. AppBrain offers both an app and a website to allow users to access its catalog. In order to download apps from within AppBrain you need to sign up, otherwise you will be redirected to Play Store.
Aptoide (link)
It has a nice visual interface and the categories and tabs looks like the Play Store. It also has a dedicated app that also detects your installed apps and offers updates if available.