The Bay of Gibraltar has one of the highest concentrations of dolphins in the Mediterranean and there are a number of companies running trips out to see them. The two most well known are Dolphin World and Dolphin Safari, both can be found at Marina Bay.
The best time is November to January and be aware that the boats tend to go into dry dock during February or March for maintenance. The cost is about £20/£25, either pick up a leaflet at one of the tourist places along Main St. or take a stroll down to Marina Bay and check out prices and times.