The most obvious ones are snakes, especially pythons, because it can take them a very long time to swallow a large animal completely. This is because they evolved to breathe while they consume their food.
Some creatures (such an anaconda) have a breathing tube that connects to their lungs in the lower jaw, allowing them to continue breathing even when their throat is closed by food. However, most carnivores can easily ingest a piece of their prey after tearing it off. They can also regurgitate it if they are unable to tolerate it for some reason.
We have a fairly narrow pharynx, making mammals the only creatures with this type of oral anatomy (back of the throat). The majority of vertebrates use a process known as “pharyngeal emptying,” in which they essentially shove a substantial volume of food down a broad, non-muscularized gullet (neck muscles aid in pushing the food down).
As opposed to other vertebrates, mammals have a muscularized gullet (those neck muscles now function as the muscles of facial expression, including the cheeks that aid in food processing), and they only swallow discrete small lumps of food (a bolus) after they have been thoroughly chewed by the teeth.
It never grows small enough to activate the swallowing reflex, which is why you can keep chewing gum without swallowing it. In conclusion, while many animals are capable of readily swallowing their prey whole, mammals are not.
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