Monitoring the Mac App Store for free applications?
You could use AppShopper to be notified of discounts of specific apps you are looking for. AppShopper works with iOS apps as well as Mac App Store apps. You can have it email you when a price changes, or you can install one of their iOS clients and have a push notification sent to you.

The nice thing about it is that you don't have to have the app running (or remember to run the app once a day) in order to be notified of price changes; it just sends you alerts whenever something happens.

If you are specifically looking for free apps, you can setup the email feature and then add a rule which deletes emails from AppShopper which don't contain "free" in their subject.