Please exclude the case of melanoma which have higher levels of basal gamma-H2AX. And apart from drugs how much can handling of a cell line affect the foci formation in the same?
I think this can be very cell line dependent. Many cancers, like melanomas (as you mentioned) and leukemias (such as AMLs), can have high basal levels of ROS. In general, it is widely accepted that ROS production increases in cancer cells, as a result of increased metabolism, possible mitochondrial misfunction, and oncogenic stimulation. I think it really depends on their regulatory pathways and if those pathways produce endogenous levels of ROS.
As Anne noted, the number of H2AX foci in any given cancer cell line vary with the origin of a particular cell line. Additionally, it may also depend on the culture conditions- if you can reduce oxygen levels for culturing cell lines to close to physiological levels (~3%), you may see reduced number of foci in the due course. Further, the presence of certain reducing agents in the medium and serum could influence the number. Considering the above possibilities, if the goal is to maintain the genetic stability in cells, a number of these approaches could help.