The Last Question by Isaac Asimov
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On a side note: if you enjoy galactic timespanning of this sort, Alastair Reynold's "inhibitors" (a "race" of machines forming the backdrop of most/many of his novels) makes for some fascinating reading from a working astrophysicist. I found myself impatiently reading through the story, trying to get to the next bit of exposition where the Inhibitors are discussed. I wish he'd done even more of this. Ah well.
It just happens with very low probability. But even very low probability events have to happen sometime, given enough time.
for example: when I read HHGG for the first time, and the parts about the Deep Thought computer, I assumed it was inspired by and/or a humourous tribute/riff on Asimov, because there were so many strong similarities in structure and narrative techniques.
I thought the ending was a really nice unification of scientific and religious thought, done in a novel way that I've never really seen before. If you don't like it, then I guess there's no other way to really argue for the story. I always thought that Asimov's strength in writing lied in his ideas, as opposed to his descriptions and writing ability.
The execution of this idea was also first-rate, IMO. The question 'can entropy be reversed?' acts as a brilliant 'hook' for the story as he fleshes out the history of the universe. He took a question usually too remote to be worth consideration in literature, and humanized it. And finishing on the Genesis quote was a stroke of brilliance.
'It takes control and slowly tears you apart.'
It resolves the apparent 'paradox' between increasing entropy and increasing complexity of life: life thrives only because of the initial low entropy of the sun.