It depends on the cancer. There are dozens, if not hundreds of documented mutations and chromosomal abnormalities that are found in cancers of different types. I used to work in a lab testing for some of the more common ones to help diagnose cancer types. If there were one single change that is always seen in cancer cells and never seen in normal cells, that would make curing cancer much, much, MUCH easier. But it doesn't work that way.
One common change seen in some leukemias (specifically chronic myelogenous leukemia or acute lymphoblastic leukemia) is the so-called "Philadelphia chromosome". This is a translocation between chromosome 9 and chromosome 22, that forms a fusion gene called BCR-abl. The protein coded for by this new gene causes uncontrolled growth of the cell.
But again, this is only seen in some types of leukemia, and not always in every patient with those types of leukemia.
Biology is complicated. Cancer biology is REALLY complicated.