I have a marriage contract of separation of money with my wife (not sure how you call it ), but I know it is not recognised legally in Japan as it doesn't exist there. How common is this in countries like the States or anywhere else ? The point of the contract is that each spouse is not financially responsible for the other, and cannot inherit from the death of the other (so if one dies, his patrimony goes back to his blood family (parents, siblings, children...), not to the spouse. If one spouse gets indebted, the other liable for him/her. Finally, it also means that bank accounts are separate and that all possesions preceding the mariage would be returned to the original owner in case of divorce. So if the husband already has a house of his own and the wife has a car, if they divorce, the husband keeps his house and the wife keeps her car. There is no divisio 50-50 of the total of possesions.
As already mentioned, pre-nuptial agreements are quite common in the U.S. though can sometimes be nullified via litigation. For example, if the agreement is created without each party having representation by their own lawyer, there is a good chance it will not be recognized by a court. Or if the divorce is precipitated by one person not participating in the marriage in good faith (like if the divorce was caused by an abusive husband).

In general, in the U.S. any property/money owned before marriage remain separate -- there is no need for an agreement for this. For assets acquired after marriage, it depends on the type of asset and the state where one resides. Some states are "community property" states where almost everything acquired after marriage becomes jointly owned. For example, one person's salary is considered owned by both. In other states one's own earnings would continue to be separate property.

Pre-nups are most common for second marriages when people tend to have more complicated situations -- they might own more assets and there are often more complicated issues of inheritance (such as children from previous marriage).

We also made some agreement before getting married but I don't think it would hold up in court if it came to that.