In species where a prominent male has a harem of multiple females. This usually involves killing not only rival males, but all of their offspring too. Here's a Wikipedia article about it: https://en.wikipedia.org/wiki/Infanticide_(zoology)

In species which keep territories, animals will kill rivals of the same species, but because it's not targeted it's not genocidal, unless the species eusocial, in which case it can result in massive genocidal wars, e.g. https://en.wikipedia.org/w/index.php?title=War_in_ants