He's been praised here before, especially for his excellent book of essays, Reappraisals, which I can't recommend highly enough.
He had a knack for bringing things to a point.
"History can show you that it was one pile of bad stuff after another," he once declared. "It can also show you that there's been tremendous progress in knowledge, behaviour, laws, civilisation. It cannot show you that there was a meaning behind it.
"And if you can't find a meaning behind history, what would be the meaning of any single life? I was born accidentally. I lived accidentally in London. We nearly migrated to New Zealand. So much of my life has been a product of chance, I can't see a meaning in it at all."
Being someone sensitive to the influence of chance on history (and the historian), I have to say that this speaks to me.
[UPDATE:] a somewhat older video of Tony Judt, at the Guardian, talking about living with motor neurone disease.