The first thing you'll realize when you start thinking about this is that to have a non-zero chance of dying you have to live forever. We're not talking about just living indefinitely long, replacing organs as you go and whatnot, but instead I should be able to name any time in the future and you'll still be around. Let's take a look at what that will take.
100 years: I'll assume you're in your early twenties right now so I have a number to work with. The longest living person that I'm aware of was
Jeanne Calment who lived to the age of 122. So, if you want to live another 100 years, you could maybe do it just with good genes and good luck. We're only looking for a non-zero chance, so we're doing good so far.
200 years: Congratulations! You've lived another 200 years and managed to break all records of human lifespan previously known. To get to this point unprecedented medical advances have been made. New organs can be grown replaced as you need them, and methods have been devised to keep your brain cells healthy, or at least to replace them bit by bit. Or maybe you do get a brain replacement every now and then, but your old memories, personality, intelligence, etc. are imprinted on it. Would that still count as you? For the sake of argument let's say sure, why not.
Almost as important as the advances in medical technology is your access to it. Perhaps this tech is available only to the rich and influential, or maybe it's so cheap and easy everyone can use it. In any case, you've managed to discover the fountain of youth, and you have a long life ahead of you.
10,000 years: A lot has changed in your lifetime. You're one of the oldest humans alive, having been lucky enough to be in the first generation that had access to effective immortality. Aging and disease are distant memories. You've managed to live through the strife caused by the end of death. Perhaps that elixir of immortality is available to only a select few, or perhaps humanity has spread beyond Earth to cope with an ever-growing population, or maybe childbirth is strictly controlled. Whatever happened society lives on, and you with it.
100,000 years: You've managed to go a thousand centuries without your head getting crushed under the back wheels of a bus. Kudos.
1,000,000 years: A million years. Wow. How much memory can the human mind hold, anyway? Do you remember your childhood, your first kiss, the face of your parents? Perhaps you have some sort of external memory. How recognizable would you be now to yourself in the year 2013AD? Are you still human, even? Whatever you are, let's say that you're still you, and you've lived this long.
You've seen the rise and fall of countless civilizations. Most of human history is in your mind. The invention of agriculture and the city happened a mere 10,000 years before you were born; at this point, that's pretty much a rounding error in your age.
109 years: The Earth is about 5.54 billion years old now. You've been around for 18% of that. When you were born there had been five major mass extinction events in Earth's history. Has another one happened by now? Perhaps a giant comet or meteor has struck the Earth in your lifetime, shrouding it in a cloud of debris that blocked the sun. Maybe a nearby star went super nova and bathed the Earth in gamma radiation, driving you and everyone else underground. Whatever has or hasn't happened, humanity must have god-like technology by now for you to have survived this long. We're definitely in the realm of science fiction now, but you said 100% certainty, so why not?
3 x 109 years: The Milky Way and the nearby Andromeda galaxy merge. You've seen Andromeda grow in the night sky from the little smudge it is today to a giant, sky filling wonder. Don't worry, galaxies are mostly empty space, so it's very unlikely that our sun will be hit by another star. You and whoever else is around will have to think of a name for the new galaxy that forms.
5 x 109 years: You're about half as old as the Earth now and the sun is dying. As it burns through its hydrogen fuel it begins to fuse helium and heavier elements. The sun expands and swallows up the planet Mercury, then Venus. You had better hope that there was a well funded space program sometime in the last few billion years because Earth is not a fun place right now. The oceans have boiled away and the surface is a scorched desert, to say the least. At noon the giant, red sun fills the entire sky from horizon to horizon. Hopefully you've invested in a nice retirement home on Europa.
1010 years: You're about half as old as the universe and Earth (and the rest of the solar system) is long gone. Has the problem of traveling faster than light ever been solved? Can you zip between stars with your warp drive, or do you just accept that trip will take a while? You've certainly got the time to travel, and if you're going at relativistic speeds it doesn't even seem to take that long to you. By now lots of good books have likely been written, so hopefully you'll have something to keep yourself busy on your voyages between stars.
1011 years: The galaxies in the Local Group begin to merge together into one giant galaxy. Guess you'll have to come up with yet another galaxy name.
1012 years: Half-Life 3 is released. It doesn't live up to your expectations.
2 x 1012 years: Remember how you had to keep coming up with galaxy names? Well, the universe is constantly expanding and all other galaxies have receded beyond the edge of the observable universe. So, since there's only galaxy sitting in the middle of a black emptiness that stretches billions of light years in each direction it seems kind of redundant to bother naming it. When you meet new alien lifeforms and civilizations you try to tell them that the universe used to be full of galaxies just like the one you're in now, but it seems a little farfetched to them.
3 x 1012 years: You and whatever's left of humanity and the other races you've met clearly have amazing powers to have lasted this long. You may as well get a hobby. Why not find a planet with primitive intelligent life and convince them you're God? Get a few friends together and get followers on different continents, and see whose worshipers dominate the world. Best RTS ever.
1014 years: Star formation ceases. The stars that currently exist burn out one by one, leaving dimly glowing dwarf stars, fast spinning pulsars, black holes, etc. The night sky (assuming you're even on a planet right now) grows darker with each passing aeon as the stars wink out of existence. You've been around a long time, and you start to feel an emotion you almost forgot the existence of; an existential fear of your ultimate fate.
1015 years: You're having a hard time finding a welcoming planet. The ones that haven't fallen into their parent stars have been flung into interstellar space, drifting forever in the cold darkness. Perhaps you and what's left of the other intelligent races have undertaken a massive engineering project to keep the light of life burning in a dying universe. You and the others build an artificial star at the centre of a Dyson sphere, a solar system sized construct surrounding your new sun. This is the last bastion of civilization and intelligent life, a flickering candle in the infinite darkness. Memories of everything and everyone that ever was is stored in vast libraries. You and the other immortals try to discover new physics to stave off the inevitable.
1018 years: You stare into the abyss, wondering if there are other bastions of civilization like yours that exist beyond the edge of the observable universe.
1020 years: Similar to the fate of the planets, stellar remnants are flung from the galaxy or begin falling into black holes. The One Galaxy grows smaller and denser, increasing the speed of this process. You and the Immortals are mindful of this and carefully plot the trajectory of your home. Perhaps you're somehow finding fuel for it to keep the star at its centre burning, or maybe you have to keep making new ones. As the last galaxy dies, you're concerned that you can't keep this up forever. You continue your study of physics; no new discoveries have been made in aeons, but you keep looking for loop-holes in the laws of nature that might save you. Many others have decided this is futile and have accepted their fate, leaving your collective to drift lifeless among the remains of the stars. You press on.
1040 years: You know protons, one of the subatomic particles that (along with neutrons and electrons) make up the atoms and molecules of all matter that you interact with? Most of them are gone by now, having decayed away in a slow but inevitable process. All regular matter that's left is a rare resource. If you've somehow, miraculously, against all odds made it to this point, you're most likely alone. Everything is cold, dark, empty, unforgiving.
10100 years: All that's left in the universe is you (somehow) and black holes. How are you even still alive? The vast majority of your existence, so much so that everything else is barely even worth mentioning, has just been you floating in darkness with nothing but black holes for company. Even they are starting to vanish as they evaporate through Hawking radiation, shrinking in mass and then winking out of existence.
Beyond: There are still some photons, electrons, and other things flying about, but the universe is so vast and empty that they hardly ever interact with each other. It's uncertain what the future holds at this point, but you won't be around to see it. Some of the electrons that were once part of you are still around I suppose, somewhere, but it's impossible at this point that anything that could be considered "you" could remain. Perhaps other universes exist or will come into existence, and if there are an infinity of them then some entity very much like you could very will exist in them, but the "you" that you are now will be gone, irrecoverably, forever. The light of life in the universe has guttered and been extinguished.
tl;dr: Maybe you can beat cancer and AIDS and aging and go live among the stars, but you'll never escape entropy.