It very much depends on the context and what you are trying to investigate. Assuming you are asking for double strand DNA breaks, there is no gold standard to quantify absolute numbers, and to do that is very difficult, if not impossible. For a relative measure at low levels of double strand DNA breaks, phosphorylated H2AX foci of 53BP1 foci work fine. If you expect lager DNA damage loads, comet assays can be useful, where you measure the tail moment of DNA escaping the nucleus in an electric field.