How good are the online tools that claim to measure bandwidth like http://www.speakeasy.net/speedtest?
I can think of no better tool for telling you how slow the slowest point between you and their test server on the Internet is than those kind of online tools. Of course there's no way to tell for sure how much of the speed you're seeing (or not) is down to your connection...
The one thing these tools appear to be even better at doing than testing internet connection speed is generating random numbers. Just ran a few tests myself, one with the site you linked to on my workstation, one with a site I've used before (speedtest.net) from my workstation (wired connection to my cable router) and a 3rd one from my iphone to speedtest.net (wireless connection to my cable router).
The results were, respectively: ~8Mb/s, 343Mb/s and 12Mb/s. None of those corresponds to the type of connection I've paid for, with 2 being too slow and one being too fast by a considerable degree. I don't think that speaks well for their usefulness.
I'd say uploading and downloading your own test file to space at your ISP (do you have a website with them that you could use?) might be a reasonable test. This is also a fair internal test.