The option to run speedtest.net from Internet Explorer on Windows Phone 8 devices is not available, so having the utility available as an application is not only useful, but an example of why applications still have their place alongside HTML5 apps and 'browsers do everything'. I wonder if some of the tools and code that the app uses are Windows Phone 8 specific, as there is no Windows Phone 7 download.
While speedtest results can never be a definitive answer, this app will give you an answer under relatively real world conditions, and keep track of the results over time and on various connections - here I can see the difference between wi-fi and the mobile network while sitting at my desk.
There are a number of apps called Speedtest in the Windows Store (which is another issue for Microsoft, but one every app store has struggled to deal with). You'll want this one.