This is a topic I thought would have a interesting discussion. Now I've always wondered, under favorable conditions can any and every species be held in a captive situation? Take narwhals for example. They have not been known to thrive in captivity, but if they hypothetically had a 100 acre pools with a chilled water cooler and anything else that they need in the wild, would it be possible?
This is completely unrealistic and infeasible. You would be setting up for failure with this set up.
Many cetacean species can be housed successfully in captivity, and as others have noted back in the 60's-80's many species were tried. The main issue is that cetacean captivity in "western" countries really only started to become competent in the late 90's, and at this point wild captures were largely stopped, so we were left with what remained, the most durable species.
Anyway, back to Narwhal. They have only been attempted once, in 1970 at the Vancouver Aquarium, all dying within 4 months. A rescue calf was taken to the New York Aquarium in 1969, but it died fairly quickly as well. These where the times when pools were small and shallow, capture methods were stressful and husbandry practices were extremely poor, as cetaceans as display animals had only been around majorly for 10 years.
I'm certain that is it was attempted now, with our current knowledge and habitats, if Narwhals were attempted again we would find much more success. For example Vancouver's current beluga habitat would be ideal.
Also to note on Spinners, there are some captive. A facility in the Philippines houses a couple of rescued females, and they've had them for almost 3 years now. Commons, there are none known to be captive currently, however there are 4 common x bottlenose hybrids kicking around. The pure animals do OK, but they require a gentle hand and are very sensitive something that was largely not catered to back in the 60's and 70's when Common Dolphin captivity was at its peak.