While they don't always take center stage in the Dragon Ball series, the titular Dragon Balls are the catalyst for many of the major events that take place. They're the reason Bulma met Goku, they're the reason Goku and friends went to Namek and they're the reason that everyone is still alive after being killed so many times.
But there's actually more than one set of Dragon Balls, and each set has its own quirks, drawbacks and even dragons. Here are what makes each set of Dragon Balls unique and how they work.
Earth's Dragon Balls - Dragon Ball
The Earth Dragon Balls are the fist-sized ones first introduced back in the original series. They were first created by Kami and later recreated by Dende after the original set was destroyed. This set summons the dragon Shenron, who can grant any wish that doesn't alter free will and/or isn't a wish he's already granted, although this doesn't stop people from wishing the dead back to life over and over throughout the series.
Even this wish has its limits, however. The person can't have died from natural causes like a heart attack or old age, and they can only be revived once. When reviving multiple people, they all must have been dead for less than one year, but this rule doesn't apply to reviving individuals. This was confirmed when Frieza was brought back after being dead for much longer than a year. The Dragon Balls also can't be used to bring death on someone more powerful than the creator of the Dragon Balls.
The reason that the Dragon Balls scatter after a wish is made is that they store negative energy equal to the amount of energy used to grant the wish, so scattering allows this negative energy to dissipate without harming anyone. Should they gathered before the process is complete, the Dragon Balls will crack and a dark version of Shenron, "Black Smoke Shenron," is summoned.
This only happens in the non-canon Dragon Ball GT, after a wish is made in succession to undo the damage from Super 17's attack. Instead of the normal wishing routine, the Dragon Balls crack and their pent-up negative energy escapes, because of how often they've been used in the series. Black Shadow Sheron swallows the Dragon Balls, then splits into the seven individual Shadow Dragons.
Namek's Dragon Balls - Dragon Ball Z
The Dragon Balls from Planet Namek, Kami and Piccolo's homeworld, are significantly different from the rest. Created by Grand Elder Guru, they're much larger in size and summon the dragon Porunga, who is able to grant three wishes instead of just one, but only once every 130 Earth days. Porunga can only bring individuals back in a given wish, unlike Shenron who can bring back multiple people with just one wish. Porunga can also bring someone back multiple times instead of just once.
Instead of scattering, the Namekian Balls turn to stone, so there's no hunting involved unless they're manually hidden. The Namekian Balls also require a password to be used and Porunga only speaks Namekian, meaning Dende is the only living Namekian that can effectively use them. At some later time, the Namekians modified their Dragon Balls to be able to bring back multiple people like Shenron.
The Black Star Dragon Balls - Dragon Ball GT
This particular set of Dragon Balls were created by the Namekian Piccolo and Kami used to be before his personalities split. Because he was the unified form of his good and evil personalities, the Black Star Dragon Balls can grant more powerful wishes without limitations and don't turn to stone after use. However, they also have a monkey's paw effect, where the planet where the wish was made will be destroyed unless the Dragon Balls are returned there within a year.
While this sounds simple enough to prevent, the task of gathering them again is made harder by the fact that the Black Star Balls scatter across the galaxy rather than the confines of the planet. The dragon summoned with this set is Ultimate Sheron. These Dragon Balls only ever appeared in Dragon Ball GT, which means they don't technically exist anymore, as that series is no longer canon.
The Super Dragon Balls - Dragon Ball Super
The Super Dragon Balls were the first to ever exist, and form the basis of every other set, as their Namekian creators shaved bits off of this set to create their own for other planets all over the universe. They are the size of planets and summon the Dragon God Zalama, or Super Shenron. Once used, these Dragon Balls scatter across Universes 6 and 7. In order to use them, the wish-maker must speak in the Divine Language and speak a specific phrase to the "core of Zalama's presence." Seeing as the dragon is many times the size of the Universes' galaxies, this is easier said than done.
The Dark Dragon Balls - Dragon Ball Heroes
Exclusive to Dragon Ball Heroes, this set is dark red with black stars. They summon Dark Shenron, and scatter throughout time and space, making them nearly impossible to gather. They can also merge with living beings and grant great power, as they do throughout Heroes' Dark Empire Saga. Making just one wish with these Dragon Balls generates enough negative energy to summon Shadow Dragons.
Cereal's Dragon Balls - Dragon Ball Super (manga)
These are the latest Dragon Balls introduced to the series. About the size of marbles, they are also the smallest. There are only two in the set as well. They feature black stars instead of the red-orange color of the Earth and Namekian sets and summon the relatively small dragon Toronbo. It seems that they have to ability to revive an entire race of people without limits, as mentioned by Granolah, but what else they are capable of and if there are side-effects are currently unknown.