General Intelligence is that which you measure when your IQ test has been optimized to remove the specific types of bias that mean that two people with the same amount of intelligence give different results on different tests. For example you might have one come out as more intelligent using one version of the test, and the other one come out as more intelligent using a different test. And this is despite the fact that they had both been screened for bias.
Latest research using twin studies and other methods seem to conclude that general intelligence exists. Furthermore, there has been a method developed that can directly measure it. This method is called Evoked Potential, and it seems to measure how fast you think.
Of course this does not answer the question What is Intelligence.
This is not to say that the specific intelligences don't exist, they do, and they are very useful.
Part of the Intelligence Project