It is a fundamental tenet of Islam that everything is permissible, except those things that have been explicitly banned. Based on this, most Muslims would agree that it is permissible to have a dog for the purpose of security, hunting, farming, or service to the disabled. Many Muslims strike a middle ground about dogs -- allowing them for the purposes listed, but ensuring that the animals have their own space which does not overlap with human living spaces. Many would ensure that the dog is kept outdoors as much as possible, and at the very least is not allowed in areas where Muslims in the home pray. For hygienic reasons, when an individual comes into contact with dog saliva, one needs to wash.
Owning a pet is a huge responsibility, that Muslims will need to answer for on the Day of Judgment. Those who choose to have a dog must recognize the duty they undertake to provide food, shelter, training, exercise, and medical care for the animal. That said, most Muslims recognize that pets are not our "children," nor are they humans. One should keep things in perspective.