COMMUNICATION IS:
The imparting or interchange of thoughts, opinions, or information by speech, writing, or signs (dictionary.com).
... interchange of information.

WE WANT TO COMMUNICATE WITH:
Any being capable of looking beyond themselves in the Universe.

WHY WOULD DIFFERENT SPECIES WANT TO COMMUNICATE WITH EACH OTHER?
To warn, to attract, to display their ability, to protect themselves, to repel, and to inform another of something they want to do.

***COMMUNICATION OF DIFFERENT SPECIES:
//VISUALLY
_Snakes, Poison tree frogs, spiders
Snakes are brightly colored with intricate or contrasting bands of red, yellow, black, white etc. This coloration serves as a warning signal to enemies. It can also confuse predators as to which direction the snake is moving, since different colors blend at high speed.
_Growling
is a low, guttural vocalization produced by predatory animals as a warning to others, as a sign of aggression, or to express anger.
_Peacocks
_Flowers (shape and color)
_Dogs
Fur stands up when in fear or unsure. Makes them look bigger and robust to deter a fight.
_Ungulates
Pursuit-deterrent signals occur when prey indicates to a predator that pursuit would be unprofitable because the signaler is prepared to escape- they hop in such a way that shows that they are capable of running away. Such signals can advertise prey’s ability to escape, and reflect phenotypic condition (quality advertisement), or can advertise that the prey has detected the predator (perception advertisement).

//SMELLS
Many mammals, in particular, have glands that generate distinctive and long-lasting smells, and have corresponding behaviours that leave these smells in places where they have been. Often the scented substance is introduced into urine or feces
_Skunks
Muscles located next to the scent glands allow them to spray with high accuracy as far as 2 to 5 metres (7 to 15 ft). The smell aside, the spray can cause irritation and even temporary blindness, and is sufficiently powerful to be detected by even an insensitive human nose anywhere up to a mile downwind. (http://en.wikipedia.org/wiki/Skunk)

//TOUCH
Defense mechanisms that provide a warning visually and also have a painful repercussion if messed with.
_Turtle
_Porcupines
Porcupine quills are as sharp as needles, detach very easily, and will remain embedded in an attacker. Unlike needles, however, the quills of New World porcupines have microscopic, backwards-facing barbs on the tip that catch on the skin making them difficult and painful to extract. (http://en.wikipedia.org/wiki/Porcupine)
_Prickly Pears/ cacti

//TASTE
_Corpse plant
_Fruit

//HEARING
_Growling
_RattleSnake


Good Explanation of Animal Warnings (http://en.wikipedia.org/wiki/Animal_communication)
Some other important notes:
Animal communication is largely by instinct, while human communication is cultural. (http://en.wikipedia.org/wiki/Human-animal_communication)


HUMAN-ANIMAL COMMUNICATION
A dog being scolded does not need to understand every word of its admonishment, but is able to grasp the message by interpreting cues such as the owner's stance, tone of voice, and body language.