Recognition of other animals is essential to all animals, whether interspecific (other species) or intraspecific (same species).
When human babies are young the will readily turn towards an upside down bowling ball template (two dots at top). This has been used in research to show that a lot of recognition is innate, and is not learned. This template idea shouldn't be surprising to most, but understanding how recognition comes around is a largely debated philosophical question. From here in a will take a more biology based approach.
Animals have radiated into many shapes and forms. The senses used to recognize others are strongly based on environment and natural/sexual selection. It would be rather pointless to have nocturnal animals rely on sight for example. Nocturnal animals have a Varity of methods used in recognition, but the most predominant would be olfactory based. Pheromones are important for animals recognizing when a member of the other sex is reproductively active, but are also important in recognition of non-sexually active animals. Many humans can recognize friends or family by smell as well, though it is usually based on artificial scents (perfumes and deodorants) or perspiration smells.
Sight is very important in animals which are active in the day. Colours are important in birds for showing health (sexual selection) and separating one bird of the same species from another. Humans rely on facial recognition to tell people apart and even are able to recognize emotional states in others. Most people were surprised when it was found that sheep can even visually recognize 50 flock members.
Sound is also very important for animal recognition. This is immediately obvious in birds where species may have wide ranges of calls, or just a few specific calls. If these calls couldn't be used to recognize other members of the same species or were confused with other species, mating success would immediately drop and may be the end of many species. Sound is also important below water in dolphin communication and above ground in bat communication.
Recognition is such a wide subject that if talking in general you cant really say much, each animals recognition and communication systems are complex and to truly appreciate them you would need to look at individual animals. Even most insects have a wide range of complex systems in place to be able to discriminate between mates, prey, predator or intimate objects.
The best you can say about recognition without being specific is that is sensual. Touch, taste, smell, hearing and sight are all important.