What is the purpose of a user's default database?

Question

As I understand it the default database is specified so that in case you don't specify one in the connection string, it will know where to start. Is this correct?

I've never seen a connection string without a database specified, is it even possible? Why would anyone want to do this? It just makes it less transparent to which database you are connecting.

In other words is there any reason to choose anything else than master as the default database?