Whether it's a mouse or a Maltese, when you bring a pet into your home and your heart, you are legally responsible for that animal's welfare. You are also morally responsible to give that pet the best life that you possibly can. There is no difference in adopting a pet than in adopting a child (except you don't have to worry about the pet quitting college on you). If you bring another life into your life, you have to provide all of the elements of a responsible pet owner.
Most of these elements are just common sense and, to the true animal lover, not considered a sacrifice in any way. Taking care of an animal is one of the most joyful things you can ever do.
Proper Basic Care
Food, water, shelter and getting cleaned when dirty are the things you are legally responsible for in pet ownership. The amount of food, water, shelter and proper grooming depends entirely on the animal and the circumstances you live in. It is your responsibility to find all of your pet's needs when you bring them to your home, preferably before you bring them home.
For example, if live in Philadelphia and want a Siberian Husky, you need to know if a Siberian Husky will be happy in Philadelphia. Even though you can give enough food, water and let the dog live in your home, if your Husky is miserable because you don't have air conditioning or you don't have a yard, then the responsible thing to do is not get a Siberian Husky.
Medical Care
Another important part of responsible pet ownership is getting your pet to a vet on a regular basis and whenever that pet is sick, injured or obviously unwell. Sadly, many people that own pets put the pet's health at the bottom of their list of priorities. For example, in 2008, a Pennsylvania puppy mill owner shot all of his dogs in the head rather than treat them for fleas. That puppy mill owner treated his dogs cruelly and irresponsibly, even though enough the dogs were given enough food and water to survive.
No Breeding, Please
A responsible pet owner makes sure their pets do not breed, by either neutering the animals or keeping the sexes separate. Although some organizations like the American Kennel Club claim that you have the right to breed your dog, you don't. You also have the right to ignore someone trapped in a burning house, but the right thing to do is to save that trapped person.
In the same way, society is trapped in an overpopulation of unwanted pets. Breeding purebreds for quantity and not quality has also dumped a lot of sickly and suffering pets on the world. Do not only the responsible thing but the right thing and make sure your pet doesn't breed. And if accidents happen, make sure you find good homes for the offspring. Don't just give them away to strangers.