They do get depressed. Killer whales/Orca whales (which belong to the dolphin family) have been known to get so depressed in captivity they kill themselves. Yes, they actually commit suicide, look up Hugo the whale. No animal like this should be in captivity, the only time they should be in captivity is if they are unable to be released into the wild or if they are getting treated for an injury or illness and will later be released.
By supporting whales and dolphins in captivity (by going places that have them like Seaworld etc.) you are supporting the barbaric dolphin hunts in Taiji and many other countries.