I actually think it lies in the characters and how there is a plot, but it's not overworked--which I'll explain in a sec.
The characters are really uncommon heroes. A lot of Superheroes--especially in the US--are tragic heroes that carry their gifts like some sort of burden. Goku, however, is happy-go-lucky, carefree, and fun. He's never angsty or gritty or edgy. The only time he's ever not joyful is when his friends and family are in danger--but even then he will ALWAYS offer his friendship to his enemies and would rather pig out with his rival than punch his face in. He doesn't fit in to most of the hero archetypes we usually see. This is why, I believe, Tony Stark/Ironman is so popular as well. Superhero personalities just sort of blend together after awhile, but having a Goku and an Ironman is pretty refreshing.
Also, since it is an ensemble cast (for the most part), everyone can have a favorite character whom they identify with the most. This also spawns lots of different ships, which only helps in a series' popularity. People are able to discuss, debate, and cheer on their characters.
This leads into what I said about the plot not being overworked. The Dragonball Z storyline is fairly simple; collect the dragonballs, fight bad guys, make wishes, make friends. That's about all there is to it. Some are very critical of it's plot for lack of depth, BUT this is precisely why it's so popular! People can easily imagine their own stories for the characters that could fit into the canon world of Dragonball. They can even imagine THEMSELVES in the story without necessarily messing it up.
I would argue that series like Sailor Moon or Gundam Wing, which were popular in the US around the same time as DBZ, do not have such a dedicated fanbase because their plots were pretty strict, with not much room for the viewer to imagine alternate storylines or couplings. The viewer is just the viewer, but in Dragonball Z, the viewer can be more active.
That's at least what I love about Dragonball Z.