I remember when I first really grasped the concept of forever. I was a teenager, lying in bed thinking about how nobody would miss me if I was gone, and how it would be nice to just stop existing forever. I started to think about how long forever really was and suddenly I truly understood it for the first time. I realized that when I'd been dead for a billion, billion years it wouldn't even be a single nanosecond in the tapestry of eternity. I felt it stretching out in front of me like a huge, dark ocean and I was terrified. I felt like I had uncovered some sort of horrible, eldritch secret nobody was supposed to know.
I remember getting up and turning on every light in the house; I couldn't stand to be in the dark. I stayed up all night on the couch reading bible passages, despite being an atheist, hoping they'd give me some sort of shelter from the existential terror. They didn't. I spent that whole summer in a kind of fugue. state, and my parents took me to the first of many doctors, who started on antidepressants. That started a long downward spiral that led me to where I am right now, posting on a support site for the suicidal.
To answer your question, the idea of an eternity of nonexistence terrifies me. I understand that it's a completely irrational fear, since once I'm dead I won't experience anything, and forever won't be any different to me than an instant. I'm just not a very rational person, I suppose.