Goku and Vegeta have one of the most complex relationships in the entire Dragon Ball franchise. When they first met, Vegeta was set on killing his Saiyan lesser. However, once Goku achieved the legendary Super Saiyan transformation during his first fight with Frieza, Vegeta saw him differently and vowed to surpass Kakarot's (Goku's Saiyan-born name) power level.
Despite the constant drive to become better than the other one, both Goku and Vegeta have learned a lot about each other and have developed a deep connection. Sometimes they enjoy each other's company as friends, and sometimes they are bitter rivals through and through, all depending on the situation.
10 Friendship: They Work Together... When They Have To
Being prideful, stubborn Saiyans Goku and Vegeta both prefer to fight alone in every situation. However, there have been a couple of times in Dragon Ball history where the two of them have put aside their pride to work together. They have been forced to work in tandem against some of their greatest foes throughout the series.
At the end of the day, they both know that keeping their home and their loved ones safe is really all that matters. Vegeta loves to play the tough guy and Goku always acts the fool, but when push comes to shove they know teamwork gets the job done. If they hadn't been able to put aside their differences, the Earth could have been destroyed on many occasions.
9 Rivalry: Constantly Trying to One-Up Each Other
The two lead Saiyans of Dragon Ball are constantly trying to out-do one another. Vegeta is actively focused on surpassing his Saiyan colleague, whereas Goku is more about improving himself in a general sense. No matter the reason, they are both eager to continue growing their power levels and becoming stronger than they were the day before.
It's this constant improvement that keeps everyone safe. If Goku and Vegeta weren't so determined to be stronger than the other, the Earth could have been in trouble well before Babidi arrived.
8 Friendship: They Look Out for Each Other
There have been a few occasions where Goku and Vegeta genuinely looked out for each other. Most of these instances have come more recently where Vegeta has emotionally evolved enough to actually care about others. During Bulma's birthday party, for instance, Vegeta catches an unconscious Goku who was falling out of the sky, keeping him from smashing into the deck or destroying the ship.
Vegeta also overcomes his Saiyan pride and stubbornness during the Tournament of Power to provide Goku with his last remaining energy in an effort to finally defeat Jiren. Additionally, Goku initially told Mr. Satan that he should give Vegeta the prize money for saving the Earth before eventually accepting it himself after Goten suggested Chi-Chi would let him train again. Goku and Vegeta have shown that they do look out for one another in their own ways.
7 Rivalry: Pushing Each Other to Improve
On the rare occasions these two train together, they pull out all of the stops to try and be the first to complete a task or land the more powerful blow in the event they are sparing. Trash talk also causes the other one to try harder at whatever they are doing.
While the banter they exchange during their training scenes is often comic relief, their sparring sessions are enough to excite even the most casual anime fan. But more importantly, it allows them to better understand each other's fighting style which makes their one-two punch much deadlier on the rare occasions they do team up.
6 Friendship: Shared Saiyan Heritage
With so few Saiyans left in their own universe, Vegeta feels an underlying need to interact with his fellow Saiyans. While Goku doesn't know any of his Saiyan past due to childhood amnesia, he does have a special bond with Vegeta. The two of them have much in common simply because they are Saiyans.
Saiyans have unrelenting pride, hairstyles that never change, and an undeniable attraction to powerful women. Goku and Vegeta were also the very first Saiyans in over 1,000 years to achieve the Super Saiyan transformation. With all they share in common, it makes sense for them to be friends, at least when the world isn't in danger.
5 Rivalry: Raising the Stronger Fighters
During Dragon Ball Z Kai, Goku's first-born son, Gohan, ends up defeating one of the biggest villains of the franchise essentially on his own. While everyone was grateful for Cell's defeat, it did end with Goku perishing as well. With Goku gone, Chi-Chi was hell-bent on getting Gohan a good education so he could get into college and make some money.
Vegeta eventually had children of his own, though whether or not it was because he loved Bulma or he wanted to raise stronger children than Goku's remains to be seen. Upon Goku's resurrection, he got another son, Goten, only a year younger than Vegeta's boy, Trunks. The two became incredibly close friends and immensely powerful at surprisingly young ages, thus continuing the Goku vs Vegeta rivalry.
4 Friendship: Fusing Together
Whether it's the use of the Potara Earrings, or correctly performing the Fusion Dance, fusion requires similar power levels and a deep connection with the person you are fusing with for it to work properly. Not only are the strength and power of the two individuals combined and multiplied many times over, but their personalities also meld together as well.
With everything involved in a fusion, it's important to know the person you're fusing with fairly well. While they may never fully admit it, the two of them have certainly developed a bond over their many years together. They don't talk much, but they understand each other very well and are driven by similar motivations.
3 Rivalry: Separate Intense Training Regimens
Typically, Goku and Vegeta train separately in different ways to try and get a leg up on each other. Even when facing the same threat, they seldom train together. Before Lord Beerus, Goku would typically go to King Kai's planet where the gravity is ten times stronger and has trained on a spaceship capable of simulating 100 times Earth's gravity.
Vegeta would typically weather his body and mind against the elements such as meditating in a raging storm or blasting through boulders and oceans. He even told Dr. Brief to build him a hypergravity chamber that was capable of reaching at least 300 times Earth gravity before exploding.
2 Friendship: They Enjoy the Same Things, Fighting & Food
These two love to fight with anyone and everyone that is capable of giving them a challenge. However, beyond enjoying a fight, they have a few other things in common. After their Saiyan traits, bossy ladies, and powerful children they also love to eat. Other than fighting, eating is their favorite thing to do.
They are always seen eating vast quantities of all foods at any meal. Chi-Chi often packs Goku a lunch for his farming work that Goten has to bring to him, which is 12 boxes of food. On Vegeta's family vacation, he and Trunks easily ate ten plates from the buffet, a wild boar, a giant fish, and part of a massive octopus —before it inked Vegeta— and were still hungry.
1 Rivalry: Reaching New Heights in Their Own Ways
During the Tournament of Power, Goku achieved Ultra Instinct, a technique so divine that the gods themselves were in awe of a mere mortal attaining such a righteous form of power. Vegeta briefly attempted to attain this power level as well before losing his patience and pummeling his opponent. Whis later confirms that Vegeta's fighting style is too calculated for him to properly learn the technique so Vegeta vows to surpass Kakarot in another way.
Vegeta trains on the faraway world of Yardrat to learn Instant Transmission among other uniquely powerful techniques only known to the inhabitants of Yardrat. Vegeta manages to learn spirit control which not only allows him to internally amplify his power to unfathomable heights but also grants him the ability to separate energy fusions, which proves to be quite handy against Moro.