Washington was well known as a breeder, particularly of fox hounds, a sport he frequently enjoyed engaging in. His dogs were apparently quite respectable, and he was delivered a shipment of fox dogs from Marquis de Layfayette (that J.Q. Adams was to deliver but he lost temporarily in New York). It is also believed that the first Basset Hounds in America were sent by the Marquis to Washington in a later shipment. But Washington wasn't alone in keeping dogs in early America.

Franklin carried a large dog to France with him, likely belonging to his son. We only have two references to it, one from a visitor writting to say they will never forget the dog after their visit with the Good Doctor Franklin, and a second of a neighbor returning the dog after it got loose. It must have been a rowdy pup, yet we have little to tell us details.

Adams was also in the club. He had a dog and it was the first to live in the White House, meaning dogs have lived there as long as presidents have. Abigail kept one of his pups as a pet as well. Jefferson, the second to live there, didn't bring his dogs.

Jefferson picked up "a chienne bergere big with pup" on his return trip from France in 1789 after having searched to find a pair by;

roving thro the neighborhood of this place to try to get a pair of shepherd’s dogs. We walked 10. miles, clambering the cliffs in quest of the shepherds, during the most furious tempest of wind and rain I was ever in.

She "pupped" on the return voyage and the furry passengers were taken to Monticello. Two years later another fuzzy pet arrived, this being a wolf that his son in law brought to study, specifically wanting to breed it with a dog (none of Jefferson's dogs were used for this purpose and the wolf was sent "down county"). Another dog arrived at Monticello a few years later, but he was believed a bad seed; his entire bloodline, save one male kept on a chain, was eliminated. He probably led to Jefferson's later statement that he would support eradication of the whole species (1811). While he may have disliked dogs as pets after his experience, they were definitely put to use as work animals on his Virginia plantation. The original dog didn't have sheep to heard as they weren't there yet, but it did take to herding the "fowl" in at night. Once the sheep were there the dogs presented a problem, at one point Jefferson ordering his overseer to kill all the dogs owned on the plantation (i.e. by enslaved folks) as pets since they were killing the sheep.

He did love pets, though, and had purchased his first in the 1770s from an enslaved man held by his father in law, John Wayles. It was a mockingbird he paid five shillings for, and he continued to have songbirds throughout his life, purchasing two more a few years later. In 1793 they naturally arrived at Monticello and he learned it in a letter, being in Philly at the time. He replied;

I sincerely congratulate you on the arrival of the Mocking bird. Learn all the children to venerate it as a superior being in the form of a bird, or as a being which will haunt them if any harm is done to itself or it's eggs. I shall hope that the multiplication of the cedar in the neighborhood, and of trees and shrubs round the house, will attract more of them: for they like to be in the neighborhood of our habitations, if they furnish cover.

He bought two more as President in 1803 that had recieved training in music to teach them songs of the time, and we think he had four at the same time in the White House (and know it was at least three). When he finally retired in 1809, he went home to his beloved mountain for the peace he sought for so long. Soon after returning he wrote;

My birds arrived here in safety & are the delight of every hour.

Birds or even the wolf wouldn't be is most extreme pets, however. Captain Zebulon Pike went on an expedition of the Arkansas River in the early 1800s and wandered into Spanish land, subsequently being arrested. When released he had come across a trader and purchased two babies, sending them to the president as a gift in late 1807. They were kept at the White House but soon outgrew their cages. Jefferson had already arranged to send them to a "zoo" (Charles Wilson Peale's museum, actually) but it had yet to happen, so they stayed in D.C. and continued to grow. Eventually the male and female went to the new home, but did not take to domestic life. One, the male, escaped and terrorized the Peales, forcing them to shoot it dead in the kitchen. The other was soon after put down as well, and both grizzly bears were then stuffed and put on exhibit. That, imo, is the weirdest pet to ever reside at the White House - but unfortunately the mammoth cheese delivered to Jefferson in Jan 1802 was gone by late 1805, so early Americans were unable to see both a massive block of cheese on the front steps and a pair of grizzly bears on the white house lawn at the same time (though it's a certainty some residents of the district saw both in their life).

E for correction of cheesy date.