Sometimes Yes, Sometimes No

Cats and dogs do not always get along. There are some cats and dogs that will never get along and must be kept in separate quarters. However, more get along than not. Normally, there is just a period of adjustment, just like humans have experience when meeting new people.

Gender Is Not a Factor

Many cat owners think that gender is a big factor when selecting cats who will get along with each other. This is not normally the case with dogs and cats, because they are different animals and usually do not try to dominate each other as do two of the same animals. As long as pets are spayed or neutered, it typically does not matter whether you choose to get a male or female cat to go with a male or female dog.

Introduce Them When They're Young

Kittens are generally easier to introduce to adult dogs or cats because they do not have any preconceived attitudes towards other animals. Instead, they are usually outgoing and get along with almost anyone.

Companions

Pets can get lonely if they are left alone for long periods of time. They may even get anxious and start to destroy things. So if your pet exhibits signs of being nervous or destructive, consider finding them a companion, whether that's another pet or a human.

Isolation

When introducing a new pet, give it its own space, complete with food and water, in order to ease it into his new surroundings. Keep him there when he is alone, then let him out when you are home. Do this for at least the first three to five days.

Source:

Petfinder.com: Adopting the Right Cat for You