Interesting to see the clash of the two different strands of futuristic thinking in this thread, ones which too rarely get combined.
Just as we look back at people dying of childhood illnesses in their millions now and feel shocked, our descendants will feel shocked at the number of us who were killed by cancer, MS etc.
As for what we'll die of, the most likely thing is starvation due to over manipulation of crops leading to famine.
A society where the latter happens is one where the production and especially the continuing development of drugs for the former, for the masses in particular, is unlikely to go on.
Provision by state health services like the NHS, and insurers in the US is being squeezed more and more tightly and the idea that everyone is going to die of pure old age, cured of everything else, is about as likely as millions going to live on Mars within the next century. Increasing economic and geographic divisions and tightening of eligibility criteria for expensive procedures and drugs are already happening, and there isn't really an huge economic possibility of this changing. Some of the very rich will still have access to these things, but the financial incentive to develop lots more will be less as large scale buyers of treatments, like governments and insurers, can afford less.
I expect there will be several decades of increasing inequality and patchiness in treatment, with some people getting amazing care, others very little compared with the expectations they grew up with in the developed world, and as resource and populations stressors increase, there will be fewer very high tech drugs developed and less done for rarer issues.
Antibiotic resistance will make transplants much riskier, more people may opt not to have them or not to carry them out.
More and more countries, and US states are legalising euthanasia which on a macro scale fits with population trends. Britain lags because MPs majority opinions on the issue are opposite to the general population's majority opinions. There is still lingering idea of life being sacred from Christianity, although that developed at a time when people surviving the things they do now, being in near vegetative states, living decades with dementia, was simply not in the picture at all, it was about basic kindness and non violence. I am sure Britain will eventually catch up although it may take a good while given that views against it seem particularly entrenched in the legislative classes. (Curiously different from those in the arts and media too.)
Similarly I would not be surprised if there is eventually more of a push towards treating people who could be got back to work again over and above prolonging existence for people with dementia. But that is not going to change straight away because of the fears related to religion and the spectre of nazis.
On a more mundane note, there may be a lot more deaths from obesity related illnesses among generations in current youth and middle age than among baby boomers. That is the way it looks currently - and I think is what a lot of media commentators would say about "what will we all die of" . If climate change related food shortages do bite in a few decades, fewer people will be obese, although there may be lingering health complications from having been so.