Mongo authentication user can't drop database

No, it is not currently possible (in version 2.4) to create such a user/permission.

Permissions on a specific database grant permissions on entities contained in that database, but not on the database itself. Cluster level permission is needed to create or drop databases.

Reference: http://docs.mongodb.org/manual/reference/user-privileges/#database-administration-roles

Grant your user the "root" role and you will be able to delete the dbs. You do NOT have to disable authentication to do this, as long as you have an admin account this will work.

use admin;
db.grantRolesToUser("adminUser", ["root"]);

Now delete the database

use databaseToDelete;
db.dropDatabase();