Same thing happened to his dad in the Namek saga. Frieza just had to kill his best friend Krillin at the end of a chain of revenge attacks (killing Dende and severely injuring Piccolo) and then go on to threaten Gohan. Bad.Fucking.Idea. Just to prove he's Not Himself, he actually pledges to make Frieza Suffer, and yells at Gohan to go back to the ship.
On that note, Goku had a similar berserk button pressed when Krillin was murdered by Tambourine, and (at least in Budokai Tenkaichi 2's GT story mode, where he isn't incapacitated for the following) when he learns from Android 18 that Android 17 murdered Krillin.
For Goku in general, hurting or killing his love ones will end in violent retribution. Frieza and King Piccolo just got the worse of it.
Vegeta gets one of these as well during the Cell saga, when Cell kills Future Trunks. Vegeta - who, up until this point, has either ignored or explicitly rejected any attempts by Trunks to reach out to him - absolutely loses it. Of course, his attack doesn't work, but it's a pretty critical character-defining moment.
Don't harm Vegeta's pride either. It won't go well for you.
Don't try to pimp out Bulma either. Goku learned that the hard way.
After Vegeta loses to Android 18 he has one of these.
In Dragon Ball Z: Battle of Gods, the first time Vegeta goes at it with Beerus, he's soundly beaten. When he sees Beerus smack his wife Bulma, though, he goes absolutely berserk and actually gives the God of Destruction a run for his money for a short while. According to several characters, in that moment he actually surpassed Goku.
Don't hurt Mr. Satan or Bee when Fat Buu is around.
Also, do not deny or take away his food. Someone will get hurt.
Don't call Chi-Chi an old lady either. Maron almost had to learn this the hard way if Roshi and the others didn't intervene.
In Dragon Ball GT, #18 goes berserk when Krillin is killed. Again. By her own brother.
Don't trash-talk Mr. Satan when Videl is around.
Beerus, the God of Destruction, have several. The first being denying him food for any reason. Another one is calling him petty or childish, usually related to the first. Also, do not disrespect him, even if he's doing it to you or a love one. Any of the above will end with a planet blowing up.
For Frieza, remind him that he lost to a Saiyan monkey or that he shouldn't focused on revenge and go back to his empire. Tagoma did the latter and ended up being thrown out of the airlock.
Super Buu, denying him sweets will end with dimensions being torn down. The same goes for anyone who is stronger than him. Vegeto took advantage of this particular Berserk Button to get himself absorbed and rescue his sons.