2 links have been added on this idea.
  1. It exists, this app lets you record sounds from your doorbell and landline and other stuff so it can vibrate and tell you when something is happening. Great idea, looks like it gets lots of good reviews too.

  2. There are a few apps for deaf people out there already, I guess one of these does light up when it hears the doorbell or other loud noises, though I doubt that you can tell them what each sound was so it learns which are important sounds or not. Someone should make an app for that, I agree.