One of the most interesting things I've discovered not too long ago is the link between aging and the prevalence of cancer.
Sure, there are instances where younger people develop it, but generally the instances of cancer increase along with age.
It is one of the reasons I have become a lot more involved in learning about biological rejuvenation and anti-aging therapies. A topic I will hopefully be (attempting) to cover here soon.
Oxidative damage has been known for a long time to cause both ageing and cancer so you are right. Alzheimer's Disease is also highly linked to ageing. It's prevalence is expected to increase substantially over the next few years