What forms of intelligence exist, and what is the best method to effectively test intelligence?
Intelligence is very hard to define, so it is unclear what exactly counts as intelligent behavior. Usually it incorporates the processing of information leading to successful outcomes in a specific environment or across a broader range of environments. There exist different aspects of intelligence, like the range of different information inputs, the ability to remember the past and adapt to past experiences, the complexity of the of the resulting behavior and the generalization capabilities across different inputs and environments. The Intelligent behavior can be observed in single individuals or in the interactions within a group of individuals, more like an emergent effect. Concerning the complexity and adaption capabilities of the observed intelligence behavior, the human species is held the most intelligent known life form, with human beings held as the most intelligent individuals.
Because of these many different forms, there are different tests concerning different aspects.
For example one can observe bacteria moving opposite to a gradient of a poisonous chemical, which proves this is information in their range of perceivable inputs. To measure the complexity of some intelligent behavior, standard complexity measures like the Kolmogorov complexity of a simulation thereof can be used, while a less rigorous measure is the number of words needed to describe the behavior. Among humans there are different IQ tests, often based on visual and language based information - which aim mostly at the generalization capabilities - perceiving regularities and differences among visual patterns, applying formal logic and other aspects.
Since the invention of the computer, also artificially intelligent systems have been created. These systems have long surpassed human individuals in terms of information storage and are increasingly stepping up towards human capabilities in terms of adaptivity, complexity and generalization. Because humans are extra-ordinarily intelligent, they are an important baseline in artificial intelligence research. Alan Turing was the first to propose a test based on a human trying to classify a conversation partner as another human or an artificial agent, just interacting based on text in natural language.
As mentioned previously, the definition of intelligence also depends heavily on the environment. The No Free Lunch theorem by Wolpert and Macready suggests that generally intelligent behavior across all possible environments is impossible. Therefore, for a test on intelligent behavior to be effective, the environment and some measure of success have to be provided to effectively evaluate the results.
You're wrong, I was thinking of different types of intelligence e.g. Emotional intelligence.