I'll give a try at answering my own question.
As Juan stated several times (see this old blog post or the reference on this Wikipedia article), Godot's name is inspired from Samuel Beckett's theatre play Waiting for Godot.
So one could consider that Godot should be pronounced as Beckett intended it; however that's a much debated question, and there is no total consensus. But really guys, use GOH-doh if you're to go with an English-like pronunciation.
Now here's some bias from a French dude: Beckett's play was (even though he was Irish) first written in French as En attendant Godot, and only later translated in English. So I think the right pronunciation of Godot is as any Frenchman would do: go-do, without particular stress on any syllable. And most importantly: no hard T at the end!