@gollum,
Yes.
Most often it is to clear competitors out of their territories.
This applies to animals of the same and different species.
Given the opportunity, lions will kill hyenas and cheetahs without any motivation of self-defense or protecting a kill.
A single hyena unfortunate enough to find itself in the midst of a group of lionesses or within reach of a male lion is a dead hyena. Only very hungry lions will eat a hyena they kill in this way. Saw a show where a pair of male lions hunted and killed a cheetah, and not for food and almost certainly not for sport. The typical prey animal of a cheetah is really just a snack for a single lion and barely anything for a pride so while lions will certainly kill and eat small antelope if given the opportunity, the cheetah isn't really a poaching threat. However, hunting is difficult business and predators fail more times than they succeed. Except in times of great abundance this has them living on a razors edge with hunger and starvation they simply can't afford to have their hunting made more difficult and any big cat roaming and hunting within a lion's territory is going to affect prey animal behavior and make lions' hunting more difficult.
Male lions that take over a pride will usually kill all of the existing cubs so as to clear the way for its own genes.
Hippos are particularly savage when it comes to territorial battles and go for their adversary's testicles. Makes sense if you want to dominate the local stock of female hippos.
Likewise, chimps are quite brutal with those they attacks during territorial wars.
Male bears have been known to kill cubs they find unattended by their mothers (again, likely a gene spreading thing) and on occasion the mother if she comes to her cubs rescue and is not of sufficient size and ferocity to drive the male away.
Nature shows often portray the various battles that occur during mating season, but rarely the ones that end with a fatality. This may be because they are rare. In most cases, if one of the combatants submits or retreats the dominant male will let it go. It might, in one sense, be wise to finish off a challenger so that he never comes back, but doing so exposes the dominant male to serious injury or death. Once the loser calls it off the safest bet is for the winner to enjoy his victory and recover from whatever injuries he may have sustained. However, this is not an automatic outcome as some shows would seem to imply. The creatures involved in these battles have formidable weapons and they are not pulling their punches. Lethal blows can and have been delivered.
Whether you refer to these killings as
murder is a matter of semantics. Not that all human murders are senseless or done for sick pleasure, but I am unaware of any species where such killings, to the extent they happen at all, are anything but extremely isolated and more than likely due to the "murdering" animal being diseased in some way. Often animals like cats and killer whales are described as "cruel" or "sadistic" for playing with their catches but there are sensible survival behaviors likely involved here too. One is the "play" is actually a means of teaching offspring how to hunt and kill or to practice the skills required. Another, particularly as respects cats, is that while the cat usually is much larger and more powerful than its prey, the prey is not harmless. Mice and rats can deliver very nasty bites. Any injury is a serious detriment to the survival of an animal that isn't thinking about receiving medical attention when it hunts. In addition to killing the animal outright a serious injury can severely compromise a predator's ability to hunt. Hunting failures lead to hunger which can lead to death due to starvation or disease. Animal hunting methods have evolved to make a very violent behavior as safe for them as possible. One of the reasons cats may play with their catch is to weaken the prey to the point where it can't strike back when the cat goes in for the kill with it's mouth. Not even a cat wants to put its face in the way of a rat's snapping teeth.