I'm on Orange, which has an app that tells you how much of your talkplan minutes you have remaining. Until recently it also showed how much of your data allowance you have left, but that seems to have been removed. This hasn't gone down well and Orange cutomers are giving it one star ratings in the marketplace in protest.
Anyway, I found an app called ...
Looks like it depends on the carrier.
If your carrier "supports" Data Sense the app will be available in settings, near background tasks.
If you carrier does not support is not currently possible to make it available.
Looks like unbranded phones does not have this support too.
I'm getting in touch with Nokia to clarify with my unbranded Lumia did not ...
From the GDR2 update Data Sense should be available on most phones like it was on WP7 as a separate app: counting data from the phones perspective. This can be different from asking the actual network provider for the remaining data in your account (which Data Sense can also do for providers that support it), but it should be able to get you going at least.
This doesn't help you (yet), but Microsoft has an application called Data Sense. Data Sense can monitor and limit your data usage. Unfortunately for some strange reason it is only currently available on Verizon Wireless.
Data Sense, which was introduced with the GDR2 update (aka Update 2), allows you to track your data usage over time. With it, you can...
Track data using for individual app over mobile and wifi connections
Set a usage limit (unlimited, one time or monthly)
Restrict background data usage when near your data limit
Use the Data Sense service to ...
Yes, this setting an be set by going to Settings -> Network & Wireless -> Mobile & Sim
From there, tap the link for SIM settings you'll then see an option to choose the fastest connection speed to use (which, on my phone, gives the options of 3G or 4G)
I had one such issue - This happens often when i view / stream videos in my lumia 1020.
Steps that i did;
1. Reset the data counter - default
2. Turn off the phone
3. Remove sim and replace it
4. Reboot the phone
5. Search network provider - and select your operator manually
6. Then select Automatic [Only if required and if the signal strength is low]
Yes, data sense measures both data usage - Cell and WiFi. In the new WP 8.1 this is clearly separated as you can see in the screenshot and if I remember correctly (haven't used WP 8.0 for a while) it counts both of them as well but without the separation
As mentioned in the comments, there appears to be an issue in the People and Me Hub on Windows Phone 7 and 8 where it uses a lot more data than normal.
Unfortunately, on Windows Phone 7 there is no way to monitor data usage on a system level. On Windows Phone 8, if you're running GDR2 (or newer), Data Sense will give you a break down of what each (system) ...
The application comes with the GDR2 update of Windows Phone 8.
It does not depend of the carrier, as long as they don't uninstall the application before delivering the handset to you because ATM there is no way to download the app from the store.
I have an unbranded trial Lumia 925 and it does have the app running perfectly with my Vodafone Spain SIM card. ...
No this is not available on Windows Phone through any of the available API's. there are apps however that make it possible to do this as stated in other answers.
For The Netherlands specific operators there are a few apps that do this for you (they scrape the data from the operator website.
the apps are Called BelStatus and are for 1 provider only
Anybody from Czech republic can use application called FUP Monitor which is free and can be downloaded here.
Credit for the idea of such app goes to @paranoid.
This is chance for anyone from anywhere - if Call Credit app doesn't support your country or your carrier, try to search your local marketplace for similar app.
Disadvantage of this approach is ...