Hello,
There are several sites that can do this, as well as programs. A test that measures the speed of your Internet connection is called a "Bandwidth test." Here are some links to various bandwidth tests that you can find online:
www.speakeasy.net/speedtest
http://pcpitstop.com/internet/Bandwidth.asp
http://reviews.cnet.com/7004-7254_7-0.html
The numbers displayed will most likely be in Kbps or "Kilobits." However your Internet service may have told you what speed you are paying in Mbps or "Megabits." So basically you will want to divide the bandwidth test results by 1000 to find out how many Mbps of bandwidth you are getting. If the test says 3000 Kpbs then that would be 3 Mbps and so on.
Good luck!