I imagine it's a very small number, likely including elephants and great apes. However, even I struggle to grasp the concept of my own mortality. I feel like most people are in the same situation. They can tell you they're going to die one day, like they're reciting lines from a book, but they don't seem to truly grasp what it means.

Elephants could easily be aware of their own mortality. They are social, long-lived, and have been filmed interacting in an interesting way with elephant bones. There was a nice article on elephants posted here:

https://news.ycombinator.com/item?id=19828113

One way is to see which animals have self-awareness or have a sense of self. But that test is difficult because we can only rely upon our human-biased perspective and hence any test we developed will be skewed towards our way of thinking/being. For example the mirror test works well for humans, but what about animals that rely mostly on smell, sound, etc?

But even if they are self-aware it doesn't necessarily mean they would be aware of their own mortality. It's assumed that most, if not all animals, live "in the moment". So it's hard to imagine an animal that always lives in the moment to think about their own mortality.

It's mostly likely that most animals aren't aware of their mortality and they don't even have the capacity to even consider it. It would be like wondering whether an ant understands calculus. They simply lack the capacity.

And finally, what evolutionary benefit does the awareness of their mortality confer on any animal? In nature, where competition is fierce and unforgiving, I doubt animals who dwell upon their own mortality outcompete those that live in the moment.