Bear with us here, but could Goten be a reincarnation of Goku in Dragon Ball? Despite claiming he's never kissed his own wife, Goku has somehow produced two children in the Dragon Ball franchise. Gohan is born in the gap between Dragon Ball and Dragon Ball Z, while Goten arrives a little later after the Cell saga. As far as Dragon Ball canon is concerned, Goku saves the Earth yet again by teleporting an exploding Cell away from the planet, sacrificing his own life and dying for a second time. Unbeknownst to Goku, his wife Chi-Chi is pregnant when this happens and she gives birth to Goten approximately nine months later.
It seems that the couple's second child was conceived during the run-up to the Cell Games when Goku and Gohan were relaxing after their Hyperbolic Time Chamber training. Sadly, Goten spends his formative years without a father, only ever hearing stories of Goku's heroics. Father and son finally meet seven years later when Fortunetuller Baba permits Goku a day-pass to the living world. One might think this was so Goku could meet his second child, alas, it was so he could participate in the 25th World Martial Arts Tournament.
A fascinating theory suggests that Goten isn't strictly Goku's son, but rather his reincarnation. Firstly, there's the timing of Goten's birth in relation to Goku's death, with the youngster coming almost exactly nine months after Cell explodes. As mentioned previously, the most likely explanation is that Chi-Chi helped Goku "relax" before the big fight, but it's almost as if Goten came into existence as soon as Goku departed the mortal realm.
Secondly, various Dragon Ball characters have noted the remarkable likeness between Goku and Goten, particularly where their hairstyles are concerned. Even Goku, who notoriously even struggles to tell the difference between men and women, notices the similarity when he comments that there's a "little me" hiding behind Chi-Chi at the World Martial Arts Tournament. Goten's parallels with his father extend to their personality traits. Both are innocent, good-natured and pure of heart, but also gullible and easily led. Goku was always duped by his friends and foes growing up, and now Goten is often tricked by his best friend Trunks. The only real difference between the personalities of kid Goku and Goten is the former's violent instincts, which come from his pure Saiyan heritage.
Reincarnation is already well-established in Dragon Ball Z. When Goku defeats Kid Buu, he requests the villain one day return as a good person, a wish heard and promptly granted by King Yemma. If this is how reincarnation works in the Dragon Ball world, it's certainly possible that Yemma could have reincarnated Goku as Goten, so that the Earth would still have a protector that wasn't being molded into a scholar by his mother. Interestingly, Goten's name roughly translates to "awakening to heaven," which could perhaps suggest a link between Goku dying and Goten's own birth.
In terms of his upbringing, it seems odd that Chi-Chi was so insistent on Gohan becoming a scholar, but trains his brother so well he turns into a Super Saiyan. This is played off as the impact of Goku's death, but could the real reason be because Chi-Chi knows that Goten is her husband's reincarnation sent to help protect Earth?
As Dragon Ball theories go, it's very unlikely that Akira Toriyama truly intended Goten to be the reincarnation of Goku, and there's certainly nothing in the anime or manga that comes close to confirming this. Nevertheless, the possibility is a fun one to consider. The timing of Goten's birth feels highly coincidental and the child looks far more like his father than Gohan ever did, while Chi-Chi adopting a completely different style of parenting isn't properly explained. One thing's for sure, Goku's ignorant enough about the ins and outs of reproduction to not ask any questions.