Keeping a lion or a tiger as a house pet is expensive, dangerous and, in many cases, illegal and/or immoral. The next best thing is having a huge cat for a house pet. They're like your own little ferocious house predator, except that they love you and play with you instead of eating you!
Savannah cats are the largest breed, but many consider them only half-domestic because they are a cross-breed of Siamese cats and wild African serval cats. Maine coons are the largest purely domestic breed. If you've got a huge cat you'd like to share with us, please add it to this list!