There may be other Apps that do it better / as well, and I have no proof that all the figures are correct, but just recently noticed that the updated version of AVG Free (the popular Anti-Virus app, from Grisoft) now has a bit under 'Performance' where it shows how much data was used by each of your Apps.
I'm on an unlimited data allowance so it is mostly academic interest when I saw that my most heavily used App had downloaded 849 MB, but if you need to keep within a data allowance, say 500 MB, then it can also warn you when you've reached a certain quantity.
There are other Apps (such as 3G Watchdog) which monior usage to help stop you being charged / exceeding your allowance, and some devices (eg Sony Xperia Tipo) have a monitor already set up, but for someone who needs to stick within a limit, and also gets anti-virus scanning, seems AVG could be all you need!
NB 3G Watchdog also monitors usage on Wi-Fi separately from the mobile network, while AVG seems only to monitor mobile network traffic. Why would it matter ? Some broadband deals include an allowance on public space "wireless hotspots" so at least you might be able to stay within your allowance if it isn't 'unlimited'.
Also, 3G Watchdog and the Sony Tipo can do more than just warn you, but can actually disable mobile traffic once you have reached the limit you have set (eg 90%) so you cannot accidentally go over your allowance and be hit by data charges (some can be quite steep - Three charges some outrageous amount on their 'mobile internet' tariff).
I plan to contact the author to see if the Wi-Fi side can be given "stop traffic" capability and whether the App can be set to display 3G or Wi-Fi data (eg for a tablet with no 3G capability).
If AVG was to record Wi-Fi data as well, it would allow people to work out who is using most of the monthly data (by watching YouTube, or TV Catchup!) at home.