Where to store database credentials in a web app?

Since you're leaving the question open to platform, I'll add that database credentials for .NET apps are stored in the web.config file. From version 2.0 and above, there is a specific ConnectionStrings section that allows for easier programmatic access to the connection string.

In addition to having IIS automatically block direct requests to the web.config file by default, you can also use an IIS command to encrypt the ConnectionString section of the web.config file. This encryption is machine specific, adding to its strengths, and the .NET runtime will also decrypt the connection string on the fly when you access it, so there is no need for additional coding in your application to work with it.

With Java, database connection pools should be passed into webapps by the container. This is in the standard declarable in WEB-INF/web.xml as resources. The same applies to mail sessions and other external resources that may vary from installation to installation. Look up JNDI for more information on this)

The nice part with this is that the application doesn't care about how to actually connect to anything outside. It will not see any passwords, because the container itself will use them.

In tomcat this is configured either from context files (e.g.) in conf/Catalina/localhost/ , conf/server.xml or - preferably only for dev environments, from the webapps META-INF/context.xml. Other environments have their own configuration location or application.

The encryption of passwords actually depends on the container. Tomcat stores them in plaintext, but the application itself won't see it. I don't know about the mechanics in other environments.

On the Microsoft stack, things can be very nice.

You create a network user account in Active Directory with almost no permissions. You configure IIS to run your webapp as that user. You grant that user read access to the web folders and files on the disk. You configure SQL Server to grant that user read/write permissions on the tables you want. And in the connection string, you instruct the db client to connect as the user account which the webapp is currently being run as.

There is only one actual user account, although it is visible in multiple places. This user account has extremely limited permissions. There is no storing passwords anywhere, even if encrypted. There is no configuration that has to be done in code for this to work (it's all in setting up the permissions).