In the movie Man of Steel, After Krypton's explosion freed General Zod and his crew, they searched for Superman for 33 years. Shouldn't they be look 33 years older than they did when they were sentenced? Most of General Zod's crew never seem to age.
Kryptons sun was a low energy red star that made Kryptonians human like on their planet. When introduced to such a young, high energy yellow sun as Earths they become super-human.
In both the Comics and LnC, it is stated that Clark's aging process slows down and stabilizes after reaching adulthood. Which I would assume applies to Zod also, as a Kryptonian lifespan is normally several hundred years on Krypton.
Through all the different incarnations, there is no "set in stone lore" answer, however the common line is due to a yellow suns rays, there is very little cellular de-generation, and it's safe to assume that Zod and Co had travelled past many different Stars in order to get to Earth
theory: Kryptonians used artifical child births and created each individual specifically for a particular task. Seen as advanced they are at genetic modeling, they might also have overcome the aging and other problems through genetic means.
edit: also, you can clearly see the change in Zod's appearance, especially in his white hair and goatee.
This is the second answer because it represents another Theory:
Kryptonians when exposed to the solar radiation from a yellow sun are energized by it. They develop endurance, strength and healing factors.
Clark Kent or Kal-El was on earth from the time his ship landed here, and had absorbed significant amount of solar radiations to develop his superman body. So the reason for his aging could be attributed to that.
Zod and his other Kryptonian Survivors took refuge on the Moon where they stayed in their ships and salvaged any machinery they could. Please focus here - that they too were in a zone where they were exposed to indirect solar radiation. So scientifically it must have had some effect on them. While direct exposure to the Earth's atmosphere and the solar radiation was a must to develop those powers (as seen in the Movie), the simple effect trace amounts of radiation on the darker side of the moon could have served for slowing their aging process. Note that Zod and his people did age, though not a great deal. You can clearly see that from the facial features - like Zod's white beard. Combine that with a natural longer lifespan than humans and solar radiation could have been an important factor in the aging.
Seems silly but remember that their ship probably travels near the speed of light, and that isn't using the Phantom Drive which bends space making faster than light travel possible. Remember on Earth, if you move closer to the speed of light, time slows down for you. So it's possible that Zod's crew have been traveling for 33 years (remember Earth years) but to them it was only 11 years, 1/3 the time. Krypton is 27.1 light-years from Earth.
Personally plot hole, IMO Man of Steel they should have emerged from the phantom zone 23 years (because who knows how long is 300 cycles, it could be anything) after the destruction of Krypton, then maybe traveling for 10 and then travel to Earth.
Blame Zack Snyder, that works too.......lol.
Search "Time Dilation - Travel at Speed of Light - Special Relativity" on youtube.
I would assume Kryptonians age at 1/2 to 1/3 the rate of humans while on Krypton. I've always liked the idea that the yellow sun would make Kryptonians age FASTER[no source or story has this], like putting more miles on a car by driving it really fast. This way, Superman would look and age like humans, even though he would live longer on Krypton.
This would explain why Superman will look older in newer movies, and why Zod and his crew didn't look much different -- Red sun atmosphere on their ship.