*Diaspora *by Greg Egan ended with the end of the universe, if I remember right, which I very well might not as I hated the book.
No, it wouldn’t.
The OP is asking about the end of the Universe, not about the end of our little local speck of real estate.
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James Blish (of Star Trek novelization fame) wrote the Cities in Flight series.
The last book ends with the end of this universe (and the beginning of the next).
Would Michael Moorcock’s Dancers At the End of Time books qualify?
Stapledon’s Star Maker covers a much broader canvas than Last and First Men, and includes the end of the current universe and, in theory, an infinite number of others.
I believe some of Stephen Baxter’s stuff also involves the end of the universe, but I don’t recall any details offhand.
Also from comics, and now collected in a graphic novel IIRC, is Gaiman’s Books of Magic series. At one point Tim Hunter goes all the way to the end of the universe.
Jack Chalker’s Well of Souls series had an end of the universe, caused when a nullifier weapon that destroyed space created an ever-expanding rip in the space-time continuum that required the heroes to destroy this universe and recreate a new one.
They do not, but it is far, far, FAR future.
I read an anthology of sci-fi short stories one time all about the end of (whatever), grouped by stories about the end of civilization, the end of humanity, the end of the earth, the end of the universe, etc., but danged if I can remember the title. If anyone else can I’d be grateful. Five or so of the stories were of the “end of the whole universe” variety.
Any and all religious-apocalyptic fiction, such as the Left Behind series, if that counts as “science fiction” (a classification which would annoy the authors to no end 
).
There was a hard SF book I read, maybe 8 years ago, about a man who loses his wife due to a terminal illness and has her cryogenically frozen, until humanity 1) Discovers the cure to her disease and 2) gets around the major problems in reviving frozen corpses. This takes him on a journey through all time, as he has himself frozen and leaves instruction to only be awoken when advancements have been made in regards to his wife. All the way to the Big Crunch.
I definitely enjoyed the novel, but I’ll be damned if I can remember the title or the author! I’ll keep trying to think of it…
I wanted to reply saying the exact same thing. That story was awesome.
Fred Pohl’s “Heechee Saga” deals with some end of the universe themes if I recall correctly, and Larry Niven’s Ringworld series has a book dealing with Pierson’s Puppeteers that indicate they have some end-of-the-universe plans. But you have to read through an awful lot of stuff to get to the end of the universe themes in both series. And more I cannot say, spoiler-wise.
Part of the tying up of plot strings in Peter Hamilton’s “Night’s Dawn” trilogy involves sending a large army of the undead to the end of the universe, to get rid of them all.
The ending of Macrolife by George Zebrowski is set at the end of the universe. It involves an attempt by the ancient life of the universe, including human descended life, to traverse the final collapse to a new universe.
Sounds like Tomorrow and Tomorrow by Charles Sheffield.
Baxter’s “Manifold” series covered the far reaches of time at points, but like you, I can’t recall details.
There’s Pohl’s Tau Zero, which is the story of a spaceship forced to keep accelerating until relativistic time dilation allows it to travel to the end of the universe within the lifetimes of the crew.
Yeh, I think at the closing of the book Manifold: Time, the main character is on an asteroid with one of the inventors of the technology (?) as they watch a civilization cling to the last vestiges of heat from one of the last dying stars in the universe. They keep skipping forward trillions of years to watch it all play out, IIRC. I think that was the same book.
That’s the one! Thanks… I don’t think I would have remembered it. I almost started digging through all my (still packed away after 3 years) boxes of books.