This is a wonderful question and as a scientist, I'm glad to see someone has been thinking about this from a philosophical perspective.
Everyone wants to find "a cure for cancer" but quite honestly, it's not as simple as that. Cancer is not just something that occurs overnight - it's usually the result of several factors going on in the body that can accumulate over time - often over years and sometimes decades. And then there is a tipping point - some final bodily insult that drives a group of cells that have been damaged over time to become cancerous.
Finding a single cure for any one cancer is tough. Even within a given cancer type (e.g., breast cancer, there is not just one single thing that "causes" breast cancer. Breast cancer tumors are very diverse and therefore they have to be seen as a class of diseases, not a single disease (I've written a hub on this). The other cancers are going to be like that as well. For example "skin cancer" is really catch all name for a group of very different cancers (basal cell carcinoma, melanoma, etc.)
There are research groups and foundations that focus putting money into studying what events can lead to cancer, there are groups that study what types of drugs or chemicals can starve or kill off tumors, and then there is research that is focused more on how to prevent cancer in the first place.
I personally recommend a group like the American Institute for Cancer Research (AICR.org). Their research focus is primarily on how to prevent ALL types of cancers. Very simple lifestyle changes can go a long way to reducing cancer risk. And the education has to start with kids and mothers-to-be.
The US has the highest rate of most cancers. And, ironically we have the most advanced healthcare system - yet we still have these high cancer rates - that speaks volumes.