Picture any time before you were born. If it's not scary or sad to think about that, then thinking about a time after you die shouldn't be any different.
If you're worried about the actual moment of transition, it's probably going to be either too abrupt for you to really react to it (accident or violence), or you'll be super tired/unconscious and it'll basically be a relief, like sleep. This isn't a guarantee, but it's pretty likely.
As far as I'm concerned, as long as I can avoid a slow, painful death, it's all good. This is why torturous murders/executions and outlawing euthanasia are the most horrible things that people can inflict on each other-- you're ruining a person's only shot at a good death.
In fact looking at causes of death: http://www.cdc.gov/nchs/fastats/leading-causes-of-death.htm
Heart disease: 611,105 Cancer: 584,881 Chronic lower respiratory diseases: 149,205 Accidents (unintentional injuries): 130,557 Stroke (cerebrovascular diseases): 128,978 Alzheimer's disease: 84,767 Diabetes: 75,578 Influenza and Pneumonia: 56,979 Nephritis, nephrotic syndrome, and nephrosis: 47,112 Intentional self-harm (suicide): 41,149
Most of the causes can last a long time.
Even a heart attack might not kill you immediately these days you might linger on for a bit due to timely medical care.
So you better be ready for some suffering just like Ivan Ilyitch.
I'm just saying!
It's weird, we all pretend like it won't happen. We do our best to live without thinking about the fact that we have a X% chance of not making it to our next birthday.
I thought about my friend from college who died of cancer a year or so ago. I thought about my parents, who are quickly approaching those scary 1-in-1XX odds of dying every year.
It's like there's this scary axe-murderer out there, who's killing people left and right, and we all just do our best to ignore him. Because there's no stopping him. He'll come for you... He'll come for all of us. The only thing you can do is try not to think about it.