We know that wizards know of a last will and testament. After Sirius dies, Dumbledore tells Harry:
“I must tell you that Sirius’s will was discovered a week ago and that he left you everything he owned.” (HBP)
So did Harry's parents have a will?
- If they did, what was the content? Especially what did it say about Harry?
- If they didn't, why not?
It's funny (or not) how all the comments and the only answer so far are limited to how the money got to Harry.
We know that Sirius inherited everything from his parents, including Grimmauld Place and Kreacher, just because he was the only surviving son. The dislike between Sirius and his parents was mutual. Sirius ran away when he was 16, his mother Walburga blasted his name of the family tree. So it doesn't seem likely that his parents would actively do something for him to inherit. Just the fact that he was the only remaining son after Regulus died was enough. As Harry's parents loved him, there is no reason to assume that they would not leave their money to Harry.
It has been tradition since long before there were written laws that the possessions of the deceased would go to the children unless specified otherwise, because that is what most parents would want. Details can vary, either equal split, everything to the oldest, or something in between, but in the case of on only (surviving) child like Harry or Sirius, this doesn't matter.
The main point is, what were the wishes of the Potter parents regarding Harry's guardians. Sirius was Harry's godfather, but he was also pretending to be the secret keeper, a dangerous job in an already dangerous time. So it was not certain that he would be available or alive to raise Harry. They should have made further plans.