So “bless you” is the phrase you could say when somebody sneezes in the US, as I explained here.
There is another thing you can say for this occasion in the US. I first heard it in 1997. It sounded something like giZAntie to my ear, and has baffled me ever since, until last year when one of my students clued me in.
Here is what wikipedia says:
Gesundheit is the German and Yiddish word for health. When a person sneezes, German, Yiddish, and often English speakers typically say Gesundheit! to wish them good health, serving much the same purpose as “bless you” in English. The expression arrived in America with early German immigrants, such as the Pennsylvania Dutch, and doubtless passed into local English usage in areas with substantial German-speaking populations. The expression is first widely attested in American English as of 1910, about the time when large numbers of Yiddish-speaking Ashkenazi Jews immigrated to the United States.
Interestingly, one of my students of Polish descent told me that Polish people also say something to the effect of “one hundred years old”, just like their brothers and sisters from southern Shandong province, China, where yours truly is from.
I checked with an English guy at work. He told me that people in England say “Bless you”. They don’t use gesundheit. I am not surprised.