It is a tough choice between cancer and Alzheimer's, but I think I would go for Alzheimer's, especially since steps towards curing cancer have already been made, whereas Alzheimer's is still beyond our reach.
Cancer. It affects too many people and I agree with Finy, the cancer in children is particularly an area I'd want to cure. My friends nephew has an incurable type of brain cancer and he's too young to go through such an evil disease.
Addiction. It has been called a disease, although I'm not sure I buy it, not enough proof yet. But if I could, I would cure us of addictive passways. Imagine, no more smokers, no more drug addicts, no more alcoholics or gambling addicts. Lung, mouth, and rectal cancer rates would drop drastically, along with every other sickness smoking causes. Liver disease rates would drop if there were no more alcoholics. And so on and so on.
I'd say Hunger.. Though it's not a disease by itself, it's the one thing that can never be satiated and that no one has found a permanent cure for.. Seeing hunger in children is one thing but seeing it in adults who are unable to fend for themselves is totally another.. Hunger is probably worse than greed because it's always there and humans (like every other organism) must always spend time, effort and resources to find a way to continuously satisfy..
You can satisfy someone's need for money, fame, properties but you can never fully cure them of hunger!
If I could cure only one disease it would be type 1 Diabetes. It is an insidious autoimmune disease that cannot be prevented, and gets a lot less attention than cancer. It usually occurs in childhood, but not always; children with t1D grown into adults with t1D. It affects everything; physical, psychological, social, employment opportunities etc for the rest of the persons life. And I mean a cure available for EVERYONE with t1D, not just the wealthy few.
Why don't I mention t2D? That is preventable/curable.
The disease to want to amass power and destroy all the love in the world - the qualities of human kindness, giving and caring for others are in danger of extinction as we become more insular and cold. If there was more love in this world there would be less common human diseases
There are several that I find hard to choose between, particularly when you know people who have been affected by them. I'd probably would put all types of cancer top of the list followed by ones affecting the brain and then the rest of the body.
I would pick mental illness, although it is not just 1 disease. To narrow it down, depression. So many mental illnesses are invisible, including depression. Many don't accept it or believe in it. Very hurtful for those suffering.