There are many sites that will test your internet connection speed, but I have never felt the need to use such a site before. This because I know my connection speed and also because there are other ways to test it than using a site that will load a java applet, or something else on my computer just for this. This was true until I have stumbled across speedtest.net. This is an extremely good looking flash site that will present the world map and we can choose to test from various remote servers located in different places around the world. The tests are done very fast and with some nice looking animations. Also there is a history kept for the tests done and we can even share the results with others, etc.
Also they are offering paid versions that can be installed on your own server (even if this is probably interesting only for application service providers, telecommunications companies, big ISPs, etc).