TestMy.Net and TBB are my goto speed test sites.
TestMy.Net gives the option for repeated automated testing and is a single thred test so tends to give it you warts and all.
I still think the TBB test is the one that provides the more useful information, although I prefer the damped flash version to the non-Flash version.
The other name you are thinking for Ookla is probably speedtest.net, although it is also used by quite a lot of ISPs. I'm pretty certain that is a flash based test though.
Speedof.Me is conceptually a really good test, however it must overstate the results. Just ran it on my 80/20 line and got the following:
Download Speed: 80.35 Mbps
Upload Speed: 20.17 Mbps
which is a little improbable.