This article is from the Dolphin
FAQ, by Jaap van der Toorn
The short answer to this is that we do not know. There is no reliable method to measure intelligence in humans across cultures, so it is not surprising that comparing humans, dolphins, apes, dogs, etc. is impossible. There are some indications of their potential: they are fast learners and can generalize (which is also true of pigs, apes). Also they can learn to understand complicated language-like commands (which is also true of the great apes).
R.P. Balda, I.M. Pepperberg & A.C. Kamil (eds.) (1998) Animal cognition in nature - The convergence of psychology and biology in laboratory and field. Academic Press, San Diego, London
R.J. Schusterman, J.A. Thomas & F.G. Wood (eds.) (1986) Dolphin cognition and behavior: a comparative approach, Lawrence Erlbaum Associates, New Jersey