A new app from Microsoft Research, Network Speed Test, provides an easy way to test the upload and download speed of your Internet connections on your Windows Phone 8 device. The app can be used to test both WiFi and mobile network connections and will measure network delay (ms), download speed (Mbps), and upload speed (Mbps). The app keeps a history of any tests you perform, making it easy to compare connection performance over time, or between two different locations. 

The most likely usage scenario is testing the speed and quality of the mobile data connection provided by your operator. LTE (4G) and WCDMA (3G) connection speeds will vary widely depending on the exact configuration of the network, your location relative to the cell tower your phone is connected to, network traffic (congestion), and a variety of other factors. 

You will never see perfect theoretical performance (e.g. HSDPA+ Cat24 at 42.1 Mbps), nor should you expect to, but the app does provide a useful way of checking what real-world data speeds are like. These real  world speeds vary greatly from network to network, but in very general terms you can expect to see downloads speeds of around 1-3 Mbps on a 3G connection, and speeds of up to 10 Mbps on a 4G connection.

Do note that when you run a test certain details are shared with Microsoft in order to "help improve our {Microsoft's] understanding of network quality and availability". By default location information is also shared, but this can be turned off. Microsoft note that the data collected is not associated with you personally and will not be used to identify you or to contact you.

Windows Phone Store description:

Network Speed Test can provide you detailed information about the upload and download speeds of your internet connections.  The App also maintains a history of the internet connections you’ve tested for easy comparison.  When you test a network connection using the App, certain characteristics of your device and the network connection will be sent to Microsoft  to help improve our understanding of network quality and availability.  If you consent, we may also collect information about your location at the time of the test.  The data we collect is not associated with you, and will not be used to identify or contact you or for other purposes like targeted marketing.

Network Speed Test is a free download from the Windows Phone Store. The app is only available for Windows Phone 8.