I remember reading the chapter on cancer from the Alberts "Molecular Biology of the Cell" and even though I understood the basics of cancer at that point I was still suprised by many aspects. I didn't expect just how messed up the genome of cancer cells could be, with chromosomes fusing or duplicating. Of course these kind of extreme changes are very often lethal to the cell, but in the cases where they aren't they also provide the base for breaking enough control mechanisms that would otherwise prevent cancer.

Most cancer cells are genetically unstable, some mechanisms that usually reduce mutation rates are broken in them. And this enables them to accumulate the mass of mutations they need to actually become cancer.

The most striking hypothesis I read in that chapter was that telomere shortening could actually help a cell to become cancerous. I've no idea whether that idea help up, but it was pretty much the opposite of what I expected. The basic idea is that for cells that have a way to evade the usual stop of cell division for short telomeres, this becomes an advantage. The cells still divide, shortening telomeres so much that it destabilizes the genome. If the cell can survive that, it gains a large amount of the kind of genetic instability that is needed for it to become cancerous.