Whales and dolphins are both from the same species of water mammals called "Cetaceans" so comparing dolphins with whales seems like the best way to start this (I don't think enough research has been done on this topic yet, probably because whales are so big).
Wild Whale Rushes To Save Diver From Giant Shark
Marine biologist Nan Hauser has been diving with wild whales for the past 28 years — but it wasn’t until recently that she could credit one with saving her life.
Science Daily: Whales and dolphins have rich 'human-like' cultures and societies
Whales and dolphins (cetaceans) live in tightly-knit social groups, have complex relationships, talk to each other and even have regional dialects -- much like human societies. A major new study has linked the complexity of Cetacean culture and behavior to the size of their brains.
Killer whales learn to communicate like dolphins
The sounds that most animals use to communicate are innate, not learned. However, a few species, including humans, can imitate new sounds and use them in appropriate social contexts. This ability, known as vocal learning, is one of the underpinnings of language. Now, researchers have found that killer whales can engage in cross-species vocal learning: when socialized with bottlenose dolphins, they shifted the sounds they made to more closely match their social partners.
What does the sperm whale say?
When a team of researchers began listening in on seven sperm whales in the waters off the Azores, they discovered that the whales' characteristic tapping sounds serve as a form of individual communication. But what are they actually saying?
Sperm Whale Greeting
This is a juvenile sperm whale named Scar who is sometimes sighted off the coast of Dominica. He is about 11 years old and has been interested in people since he was a calf. This was the third time I had been in the water with him, and he seems very enthusiastic to see me! This was shot with a Canon 7D in an Aquatica housing with a Tokina 10-17 lens.
Two Beautiful Humpback Whales Dance | Animal Attraction | BBC - Male humpback whales repeat each others songs and add to them so they become ever more complex and beautiful, showing off their memory and sheer volume. Taken from Animal Attraction.
Close Encounter With Blue Whale At Dana Point
Science Bulletins: Whales Give Dolphins a Lift
American Museum of Natural History: Many species interact in the wild, most often as predator and prey. But recent encounters between humpback whales and bottlenose dolphins reveal a playful side to interspecies interaction. In two different locations in Hawaii, scientists watched as dolphins "rode" the
Beluga Whale Intelligence and Problem Solving - Examination of Unfamiliar Objects
Janet Mann on the Intelligence of Dolphins and Whales
Amazing Facts About Whales!