Well, there's one obvious answer: what it feels like to be dead is the same as what it felt like before you were born. But I want to elaborate a bit, as this is something I've thought about quite a lot.
First, the universe appears to follow a certain pattern. Essentially, everything that is born will die. I'm in the camp that finds this observation to be a beautiful thing; it makes everything that much more special.
What Oryx said ties into my assumptions about what death might be like:
I would believe it feels like dreamless sleep - you drift off and then you're awake again, with no sense that time has passed other than how tired you feel and the light in the room. You don't lie there waiting in nothingness to wake up, the time just skips.
So I think it would be like a timeskip...but forever.
As human beings, we have two 'selves', so to speak. We have a unique self, which was born, and will die, and will never be duplicated in the entire history of the universe. No one will ever walk where you did, when you did it, and experience life from your perspective.
But we also have a component that is not unique, in fact it is common to every person that's ever lived. That's I-Amness - which is the feeling of being, or consciousness as such. In your life, your feelings will change, your environment will change, everything will change
except for the sensation of being an 'I'. I believe it was Schrodinger who said something to the effect that the overall number of 'I-Ams' is one.
This relates to Oryx's comment in that the yogis who have allegedly learned to carry wakefulness through the dreaming state and into the deep, dreamless state have reported a feeling of a vast Emptiness that is radiant and blissful. This is more or less what it feels like when you rest in I-Amness in meditative practice.
Now, I haven't yet researched the claims of said yogis or their methods of introspection, but I regularly practice I-Amness meditation, and my experiences are the same as those reported by other practitioners.
Recently, I have become driven to have a constant mindfulness, and to learn to carry wakefulness through the dreaming and deep dreamless states. When I cross death's threshold, I want to do so consciously, and cultivating awareness seems like the best bet.
Plus, I spend a third of my life asleep, why not learn to do something constructive with that time? Not to mention lucid dreaming is just about the most fun you can have while asleep!
Different stories and accounts and also personal things lead me to believe that not only is there something beyond suffering, but something far more amazing than this.
While I have heard third-hand accounts of different experiences and consider those as well, the thing solidifying it for me was my paternal grandmother... At one point about a year before she died (in 2000) she had a near-death experience but was brought back to life.
In that year her behavior shifted dramatically; she wasn't afraid anymore, and wasn't scared, as if she had decided something. My father tells of his first-hand memories of her giving away nearly everything she owned, and my mother tells that when I was there (aged 2 or 3) that she explicitly took us shopping to buy me two suits without providing reason other than "every good boy needs two suits".
I feel the same way you do about life. As Walt Whitman said, to die is "different from what anyone supposed and luckier."
I take your grandmother's story as a sort of confirmation that I'm on the right track. The pattern of human cognitive growth is essentially one of dis-identifying with your current perspective, and then re-integrating that narrow perspective into a new and more expansive awareness. And the final dis-identification, naturally, would come with the death experience.
My roommate told me about a co-worker who was clinically dead for several minutes. The co-worker described the experience as 'shedding his body, as you would an overcoat'.
I hope to grow and evolve sufficiently that I can stably inhabit such a transpersonal space. As the saying goes, "If you die before you die, then when you die, you won't die."
