How many generations back

I don't know of any country that will take great grandparents as a reason to give you an ancestry visa or citizenship. Grandparents are as far back as they will go.

Italy will go back further than grandparents when granting citizenship, but that's not much use to you. In your case, UK and Ireland only take into account grandparents. Germany only goes back as far as the parent.

Thanks all.

I think Germany makes an exception for German Jews who lost their citizenship during the Nazi era. I'm not sure this applies to you, but if you have relatives who fled from the Nazis, this avenue might be worth looking into.

That is true, but they still generally only go up to grandchildren of German Jews who lost their citizenship. And even then, they will look at whether the ancestor could've lost their German citizenship for reasons unrelated to the Nazis. In other words, they'll make things difficult.

As said above, Italy gives citizenship to unlimited generations, if it´s the father line of ancestry. My great-grandparents were Italians and I´m doing the citizenship process in Italy this year.

germany does- at least for Russians of German descent at least. Not sure for others of German extraction.