Llamas in the mountainous regions of Europe? Alps, Pyrenees, Haemus, etc.
One possibility that fascinates me would be elephants being introduced in the Americas. How would they fare, specially in savannah-like climates such as the Cerrado and the North-American midwest?
The Midwest is cold for elephants. Anywhere that you could call "the Midwest" with a straight face is cold, miserable, and often snowy for months in the winter.
There's an elephant sanctuary in Tennessee, though, and they do very well with heated barns in the winter (both African and Indian). I don't know how well the Africans will do, but Indian elephants should do just fine throughout the kinda-lower Mississippi (not the delta region, but stretches above it), and maybe much of the South along the Atlantic coast as well. African elephants might do well in southern California - at least before mass settlement. Indian elephants could notionally prosper in much of the rain forest in Central and South America, and Africans in the Pampas and Brazilian cedrado, and maybe the Venezuelan llanos.
I could see extensive introduction of llamas to North America, Australia, New Zealand, parts of Africa, etc. as part of various gold rushes.
Camels in the American Southwest and Mexico.
I wonder if we couldn't see coyotes introduced to England as a sport animal in the 18th century. Once coyotes got introduced anywhere in Europe I'm sure they'd spread like wildfire.
I'd love to see kangaroos in North America, though I'm not sure why they'd be introduced - a failed ranching initiative like with the emus?
People like to talk about how there are so many tigers in captivity in Texas - if they got loose and some of them managed to make their way south, I bet they could establish viable populations in Central America. Because the Darien Gap wasn't already impassible enough.
Atlantic salmon are being increasingly farmed in the US Pacific Northwest; as far as I'm aware, none have escaped yet, but it could happen.