Laws of Hospitality, also referred to as Obligations of Guest and Host, Old World Code of Conduct, Rights of Hospitality, Guest Rights, or Manners, are a sacred pledge of courtesy, safety and guest privileges in the Old World supernatural community. They're first mentioned in Storm Front.
While I am here, I am bound by the same traditions as would apply were I your invited guest. I will offer no harm to anyone you have accepted into your home, nor take any action which would be considered untoward for a guest. I will report nothing of what I see and hear in this place, and make every effort to aid and assist your household and other guests while I remain.— Cat Sith
The Code of Honor of the Old World was accepted and expected when negotiating between various supernatural factions. The Obligations of Hospitality and a Sworn Oath are more binding than the threat of violence. A being making such an oath would be obligated to protect the other person from themselves and others making a threat. Failing that duty would be a serious loss of face and respect. Word would get around. In fact, they are almost holy to the Supernatural world.
The Fae, in particular, set great store on forms of courtesy, etiquette, and the relationship of guest to host; proper forms are ignored at great risk. The Sidhe, the Lords of Faerie are likely to have extreme reactions. Further, the Code rules that problems are settled face to face amongst quarrelers. Supernatural fights in the open calls human attention who, as history tells, will band together and kill supernaturals indiscriminately.
Traditional courtesies are respecting safe passage and losing to a guest with grace.
In the series
In Storm Front, Harry Dresden asks Bianca St. Claire questions about Jennifer Stanton and she immediately attacks him. To calm things down so they can talk, Dresden invokes the Old World rules of courtesy and hospitality. He even pulls out her chair for her.
In Grave Peril, Kyle and Kelly Hamilton presented Harry Dresden outside his apartment with Susan Rodriguez present with an invitation to Bianca St. Claire's ball—the safety of all guest being assured. After they leave, Rodriguez wanted to go believing it will advance her career to interview vampires. Dresden told her that Bianca has a grudge against him and would find a way around the Laws of Courtesy and Hospitality, adhering only to the letter and not the spirit of the Code. During the Ball, Kelly Hamilton touches Michael Carpenter and her hand burns. Kyle Hamilton threatened to start a fight over it until Dresden reminds him that he wouldn't want to break the Laws of Hospitality. Near the end, after Bianca St. Claire had laid a trap for Dresden by having her vampires bite Rodriguez, an uninvited guest, threatened to start a war on the grounds that Dresden broke the Laws of Hospitality by burning her house up, unless Dresden left Rodriguez to her to change completely into a vampire. She is backed up by Paolo Ortega, emissary of the Red King. Thus started The War between the Red Court and the White Council.
In Changes, Harry Dresden struggles with the fine line of not trusting his Godmother, the Leanansidhe—who is an intruder in his house and cocooned Susan Rodriguez and Martin—and the proper forms of courtesy, host to guest etiquette. Dresden requests that Lea release Rodriguez and Martin, saying that they are his guests in his home.
The whole issue of obligations and responsibility as guest to host and vice versa was something Dresden considered closely when Dresden sat down in Donar Vadderung's office. Dresden was pretty sure he knew who he really was and that he was known to test people on how well they upheld the traditions. He'd reward the faithful and send a hideous demise to the miserly, callous, or cruel.
Dresden and Rodriguez fall through a Way into the Erlking's medieval dining hall filled with by goblins surrounding them. The Erlking says: "I trust that you will be patient whilst I blow dust from the old courtesies." Then he kisses Rodriguez's hand complimenting her as a huntress. He also compliments Dresden for being an interesting quarry. Then Dresden assures the Erlking it was "chance not design" that brought him there and says: "I am humbled by thy generosity in accepting us into thine home as guests. Mine host." The Erlking is amused that Dresden caught him in his own words, courtesy is not his "close companion" and Dresden would have the advantage in a duel of manners. "This hall honors cleverness and wisdom as much as strength." 
In Skin Game, Harry Dresden goes to talk to John Marcone and finds him with Mab as his guest. Dresden offers Marcone diamonds in reparation for the death of one of his employees, and tells him that if Marcone doesn't accept "Then you and I are going to have a serious problem. Right here. Right now." Mab's eyes widen; if the Winter Knight attacked Marcone while Mab was his guest, she would be completely disgraced and her name and reputation would be destroyed. Marcone accepts the offer, but comments that part of the reason is that he doesn't want to cause problems for Mab.