The California condor is an example. It is one of the largest birds. You can say the same thing for the humpback whale. Less common, but probably more important, is the feeling that some species need to be protected because they are important for other species. The existence of many species is tied to the survival of one species.
Some trees serve as an example.
Preserving a forest may be the only way to save a bird species, such as the spotted owl. Look at the population decline in these two species. The Rhino has been killed for its horn. There has been an immense market for the horn in China. There is a massive protection effort, including purposely sawing off the horn of living animals so that there is no purpose achieved in killing them.