I think aggression and behaviors towards others important to know, along with any quirks. Do they get aggressive over food or are they laid back? Is there a certain type of person or animal that they might be a bit more wild around? For example, as sweet as my dog can be, she went through a period where she didn't like men or children very much, and sometimes she would also get a herding instinct when she saw someone running. Anyone I have ever had watch her has been given this information. They've also been warned about her vendetta against vacuum cleaners and similar tools. Other than that, the basics are good to know. Size, health, allergies, and typical attitudes so that if I see something out of the ordinary, we can communicate.

With my pup, typically she gets three or four walls a day, and longer walks on weekends. There are quite a few trails nearby as well as a dog park. This is also coupled with at least an hour of play time. She isn't a rough player, usually preferring to have the intermediate of a toy between us, but I have experience with dogs that are rougher.