An obvious example are alarm calls, in which one member of a herd or other group will alert its fellows of a predator or other threat. Another are the distressed 'separation calls' that young mammals use when they can' find their mother. And then, of course, there are mating calls, or aggressive roars and the like intended to intimidate a rival.
But there are also peaceful, non-sexual, contact calls whose primary intent appears to be simply maintaining the cohesion of the group. For example, meerkats regularly use calls to decide when to move on to new foraging grounds, keeping the group together using the principle that if three or more members 'vote' to move by making the appropriate call, then everybody moves at once. African elephants can even use long-distance communication to maintain social bonds with individuals that may be literally miles away.