In video games such as Europa Universalis and Crusader Kings, you need a casus belli to start a war. Often, to get a casus belli, you need to forge a claim on another kingdom's province. It this something that actually happened in history, rulers forging claims?
Oh yes!
We have a lot of charters (land grants) surviving from the early middle ages, most of them preserved by monasteries as official records of the land those monasteries had been given to prove their right to continued ownership should a dispute arrise in the future. Since the early modern period, it's become increasingly clear that many of these documents were faked.
The most famous example is the Donation of Constantine, a document through which Constantine gave an enormous amount of power to the bishop of Rome (ie the pope) in the 4th century. The papacy used this document to assert their authority over western Europe in the high middle ages. But in fact, it had been written in the 8th century, not the 4th, and was a clear forgery. This was discovered in the 15th century, when medieval scholars demonstrated clearly that the charter's language was clearly early medieval latin and not the language in which Constantine would have written the grant.
Since then, many more forgeries have been found. It's necessary whenever you're relying on charters as a primary source to first check whether the documents are authentic; enough are fake that you can't assume (and some of the forgeries have only been discovered recently, and are presented as authentic in older critical editions; for example, there's a fake 10th century treaty between Edward the Elder and Guthram, forged in the 11th century, presented as a real 10th-century document in the 1840 Ancient Laws and Institutes of England).
Of course, these fakes only worked because there were plenty of real charters being granted; I don't mean to suggest that everything's a forgery. But it was a real issue.
One of the most famous controversies is over the papal bull Laudabiliter (1155) which purports to be a letter from Pope Adrian to King Henry II granting him dominion over Ireland. The text cites the Donation of Constantine as the basis for the Pope's claim.
No one is sure if the text is genuine. There was a papal bull sent to England about Ireland but many scholars think that it was modified during copying at the court to strengthen the Norman claim.
There is a summary here