I find this a pretty interesting mega article on the subject
http://en.wikipedia.org/wiki/Cetacean_intelligence
There is no universally agreed definition of "intelligence." Some research shows that dolphins do have high cognitive capability meaning that they are able to recognise self and understand concept such as more or less in term of numerical continuity (but not necessarily count). [11]. Dolphins have also been recently discovered to be capable of discriminating between numbers [12]. However, a commonly used definition is "the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly, and learn from experience." This definition is separate from social/communicative traits or the ability to learn tricks (which can be done through conditioning), which many laymen confuse with animal intelligence.
Many scientists now tend to rank dolphins about the level of elephants in "intelligence" tests and say that dolphins haven't shown any unusual talent with problem solving compared with the other animals classed with very high intelligence[13].
Whereas apes can merely touch the mark on themselves with their fingers, dolphins show less definitive behavior of self-awareness, twisting and turning themselves to observe the mark.
On Self awareness...
As a further response to these criticisms, in 1995, Marten and Psarakos used television to test dolphin self-awareness [21]. They showed dolphins real-time footage of themselves, recorded footage, and another dolphin. They concluded that their evidence suggested self-awareness rather than social behaviour. However, this study has not been repeated since then, the results remain thus uncorroborated.
So Basically they are bellow primate level of intelligence. But they are pretty intelligent.
if i would bet on which of them had a bigger chance of reaching such level i would bet other primates or even animals who spent time with humans like dogs... All constant communication with humans for so many thousands of years must have some effect on them...