As other answers have mentioned, there are numerous sites offering this. However, all those are showing you which is the cheapest day to buy a flight now. This allows you to find a low price but those may not be the lowest prices because it is highly likely that purchasing the same flight a different day comes to a different price.
Instead of doing the search now, you can have a service searching for you. These are called Flight Alerts or Travel Alerts. You subscribe to a service and set some parameters, such as origin, destination (can be specific or broad) and frequency of alerts. You can also allow them to select the cheapest dates or give constraints such as weekends, months, etc (depending on the service).
If you are keen on getting a certain flight, you can ask for daily alerts and every day you will get an email that lists the cheapest flights to your selected destination. You can choose weekly alerts to diminish volume of email but you might miss the very best price in that case. The main service I have used for this is Kayak and that in fact purchased from the alert email several times. There are a lot of flights to discard though since you cannot constrain the duration of the trip or just because some might be overly complex for your tastes.