China in particular has a history of gifting Pandas as gifts, mostly loaning them to zoos and getting then back a few years later. Any Pandas born during this time of the loaned Pandas would belong to China. The earliest recorded usage of this was Empress Wu Zeitan of the Tang Dynasty to the Japanese Emperor.
The Dutch East India Company gave animals as gifts or tribute on several occasions. They even shipped a dodo to Japan, though unfortunately it is unknown what became of the beast after it arrived in Nagasaki. It may have been sold to a local nobleman, given to the shogun, or died.
To the Chinese emperor they gave, on two occasions during the 17th century, Persian horses, casuari and two small oxen from Bengal, with a cart to drive the emperor around in. According to the Dutch emissaries the emperor (a teenager at the time), was quite taken with the oxen and horses.
The Portuguese went one better though, they shipped a lion from Mozambique, to Beijing, after the Jesuits there had told them the emperor would quite like to see one.
Embassies and illusions: Dutch and Portuguese envoys to K’ang-hsi, 1666-1687
Can someone shed some light on a tangentially related story of a monarch (I believe) gifting animals to people in order to bankrupt them, the expense of caring for the animals being so great?
I remember just enough about this story to be unable to google it...
In 1861, King Rama IV of Siam offered the United States elephants. In reply, President Lincoln politely wrote:
"I appreciate most highly Your Majesty's tender of good offices in forwarding to this Government a stock from which a supply of elephants might be raised on our own soil. This Government would not hesitate to avail itself of so generous an offer if the object were one which could be made practically useful in the present condition of the United States.
"Our political jurisdiction, however, does not reach a latitude so low as to favor the multiplication of the elephant, and steam on land, as well as on water, has been our best and most efficient agent of transportation in internal commerce.
"I shall have occasion at no distant day to transmit to Your Majesty some token of indication of the high sense which this Government entertains of Your Majesty's friendship."
Harun Al-Rashid sent an Elephant to Charlemagne as a diplomatic gift and apparently it worked out well as relations between the Franks and the Abassid Caliph were improved by the exchange of gifts. source: The Great Sea: a human history of the Mediterranean by David Abulafia
There's a record in Sanguozhi (Record of the Three Kingdoms) about the then Prime Minister of China, Cao Cao, receiving an elephant as a gift from a southern vassal/ally of the time. This would have been around 200 AD.
The records goes that the Prime Minister (who essentially headed the Chinese Empire at the time) was curious about the weight of the elephant and wanted a way to weigh it and challenged those around him to figure out how, which his young son solved by putting the elephant onto a boat, marking how low the boat sank, and then putting rocks onto the boat until it equaled that mark (ie. Archimedes' principle).
Whilst the records didn't state explicitly how the Prime Minister felt about this move, he was obviously curious enough regarding the elephant to come up with the challenge to his subordinates.
I think the gifts of exotic animals were quite common in Europe in the Medieval Period and later.
Charlemagne had a menagerie of exotic animals including elephants, lions, etc. Many of the animals were gifts.
The Tower of London housed a Royal Menagerie for many centuries. Again, many of the animals were gifts from other leaders.
The same thing happened recently to my country, Belgium. It actually caused a minor political row when it turned out that the pandas were being sent to a privately owned zoo in the home town of the prime minister and not the national zoo.
The reception in this case wasn't entirely positive by everyone. The main opposition leader even dressed up as a panda at a big televised event at the time.