In the comics, yes Earth-2 Superman from Pre-Crisis was growing older. He had some grey in his hair.
On the "He's immortal side," we find out in
DC: One Million that
our Superman, leaves Earth in the care of his heir, Superman Secundus, after Lois dies. In the 700th Century he returns and enters his new "Fortress of Solitude" (We call it "Sol"). In the 853rd Century, he emerges and is rejoined with a clone of Lois and goes to live on "New Krypton."
However, as previously stated, in
Kingdom Come, he was aging as a normal human, and was similar to Earth-2 Superman in that regard. Interestingly enough, though he is older, this also makes him more formidable, as Kryptonite no longer affects him.
There was also a time around 2000 when Superman and Wonder Woman spent 1,000 years in another dimension fighting against evil. I guess you could claim that it was the dimension which kept him young, but there's no evidence one way or another.
It seems that, when pressed, unless it's Elseworlds, Superman will stay relatively young as long as he can continue to absorb yellow solar radiation. In addition, we've also seen how he'll become more powerful due to the years of exposure to said solar radiation.
A "
Captain Ersatz" version, Mr. Majestic, has been alive for thousands of years as of the late 20th/early 21st Century. According to an Alan Moore story, he is present at the death of the universe, as everything cools down to absolute zero. While a Kherbium, instead of a Kryptonian, I include him due to the fact that Jim Lee always intended for him to be an Ersatz-Superman.