Assuming Superman doesn't die in battle, and lives out his life under the effects of our yellow sun, what is his expected lifespan? Has DC Comics ever provided or suggested an answer?
There is definitely no consistency in how long he is expected to live.
As Dharini said in DC One Million he is alive:
In the DC One Million series (1998), Superman's Fortress of Solitude in the 853rd Century resides within a tesseract located at the center of Earth's sun. By this time, Superman has lived in self-imposed exile within the Fortress for over 15,000 years.
In the Kingdom Come Epilogue he seems destined to live for a little more than 1000 years.
In the epilogue, Superman is shown to have survived 1000 years after his return, and as an old man, he watches the fly-pass of the future generation of superheroes.
In the Batman Beyond episode "The Call" the 50 years in the future Superman is shown to have grey highlights in his hair, suggesting that he may only live to be 200 or so.
Bruce Wayne: I could use some Kryptonian DNA.
Superman: You'll outlive all of us Bruce, you're too stubborn to die.
In the TV series Smallville in the third season a highschool kid who has the power to see people's deaths touches Clark Kent and sees him just traveling on forever. The implication is that in the Smallville universe Superman will never die.
Paperjam makes the point that Superman may die as soon as the Sun transforms into a Red Giant. Superman could ultimately leave to a different yellow star if his intention it really to live forever.
I can't find any canon sources which states his actual lifespan under the yellow sun, but in the 1998 comic story "DC One Million", Superman was shown to be alive in the year 85,271. So he could live at least that long.
But he is hale and healthy then, so it might not be the maximum.
Actually in Smallville it was mentioned, when Clark meets Dr. Fate and Dr. Fate says he will outlive everybody. And I'm pretty sure with the boy, it literally meant Clark will live forever. Plus, there was that future thing where Clark sees his future from that old lady. Remember in season 1 or 2 he sees that:
"I will outlive everyone I love".
I don't think you're going to find one consistent answer. It has changed wildly over the years. I think the best you're going to be able to do is compile a bunch of examples of the different ways Superman's aging has been portrayed.
As one example, the Batman Beyond Universe shows him aging relatively normally.
Here he is in an episode of the original Batman Beyond cartoon:
You can see that his hair is starting to gray, implying that he does indeed age.
This is continued in the Batman Beyond comics:
The above is technically a Superman from a parallel universe, but he looks the same as the Superman from the regular Batman Beyond universe.
In a Smallville episode, a boy sees how people will die by touching them; and when he touched Clark, he saw nothing but a cape flying, and not him dying. He said to Clark, "like you have no end."