From App Engine, you can easily access other Google Cloud Platform services such as Cloud Datastore, Cloud SQL, and Cloud Storage. You can also choose from a variety of other cloud or third-party databases to use with your applications.
You can use any external database that is supported by your language if that database is accessible from your App Engine instance. These third-party databases can be hosted on another cloud provider, hosted on premises, or managed by a third-party vendor.
Google Cloud Platform storage services
For improved performance of your App Engine apps, you should use a GCP hosted database option.
Here are some tutorials on how to use Google Cloud Platform storage services with App Engine:
See a complete list of the GCP storage products on the Cloud Storage Products page.
Other cloud providers
App Engine apps can connect to external databases that are hosted on other public clouds as long as those database servers and your firewall are configured properly to accept connections. Your App Engine app connects over the Internet using that external service's public IP address.
Databases managed by a third-party vendor
There are many vendors offering managed database services such as mLab for MongoDB, Redis Labs offers hosted Redis caching. These vendors handle hosting, configuration, and maintenance of databases. App Engine can connect to these external services over the Internet, in the same way as other public clouds by using that service's public IP address.
If you have existing on-premises databases that you want to make accessible to your App Engine app, you can either configure your internal network and firewall to give the database a public IP address or connect using a VPN.
App Engine can be configured to automatically scale your application horizontally based on various metrics. Unlike web applications, databases often require non-trivial changes to respond to scale. In production applications, App Engine can quickly overwhelm a database during traffic spikes. You should take the anticipated average traffic load and load during spikes into consideration when configuring and deploying databases.