An example is horses and camels in North America. Both these species evolved in North America but native populations are now found elsewhere. Volant vs. nonvolant species. Few non-flying animals can disperse long distances. Usually, these are larger animals but not always.
Some invertebrates can migrate for long distances.
Vegetative islands in the Amazon River are an example. Other propagules, such as certain seeds and spores, may be carried by wind and water for long distances. More passively, the larval stages of many organisms can drift for long distances in the oceans. Hitchhikers-parasites, internal transport, modern transportation. Determining the mechanism of dispersal is usually a fascinating detective story fraught with chance and random success.