Why don't Saiyans age? I have seen many Dragon Ball series like Dragon Ball, Dragon Ball Z, Dragon Ball GT. One thing remains same is that Saiyans never look aged.
The last episode of Dragon Ball GT shows Pan as a grandma, but Goku was looking as young as he was in Dragon Ball Z. Why don't Saiyans age?
To my knowledge, they do age, just very slowly in adulthood. This is a genetic trait, I assume, to reach longer duration of physical demands. They are designed to be fighters, and longevity of a lifespan is only practical. Vegeta confirmed this towards the end of DBZ: "So they can fight longer". 

From a quick Google search:


  According to the Daizenshuu, Saiyan's lifespan is about the same as an average Human (70 to 90 years, with exceptions, of course), but keep in their peak longer. Unlike Humans, Saiyans remain in their youth and prime much longer. As explained by Vegeta near the end of Dragon Ball Z, they stay young longer because they live for and are built for battle


From Saiyan article on Dragon Ball wiki. (Visit the link for more examples, and a more definitive explanation).

Something else to consider: they stay in their prime longer because they are full Saiyans, whereas Pan is only quarter Saiyan.