You can create a scheduled agent to send you an email.
If it is a mail-in database, set the agent to run "If new mail has arrived".
Otherwise, set it to run "If Documents Have Been Created or Modified". To receive notifications for newly submitted documents only, you can use a notification flag field in the document and create a view to hold documents where that field is blank. The agent selection formula should specify that it runs on documents in that view only.
Your agent can use simple actions to Send Mail. You can write a formula for the Subject field that contains the name of the document's creator and whatever else you want it to say.
If using the notification flag method, have a simple action after the Send Mail action that sets the value of the notification flag so the document will drop out of the special view after the email is sent to you.