I also would recommend the experience at the Georgia Aquarium in Atlanta - as contrived as it may seem, the artificial environment is larger than a football field and more than 30 feet deep. It is the largest tank in the world at more than 6.3M gallons. The water is crystal clear (of course) and you are guaranteed to get to swim with 4 whale sharks, two mantas, hammerheads, blacktip reef sharks, sandbar sharks, sand tigers and zebra sharks as well as literally thousands of other specimens. While it may not be as "pure" an experience as a chance encounter in the wild, it is no less overwhelming and humbling.
There are many people who dive their entire lives hoping to encounter a whale shark and who just are never in the right place at the right time. At the opening of the aquarium, Phillipe Cousteau was on-hand and he reportedly was quoted as saying that in all his dives around the world, he has never had a close encounter with one.
The cost is about $300, and they supply you with all the gear (they don't want to risk any contamination by allowing outside equipment). It is a first-class experience and they treat you very well, the people are highly trained and very knowledgeable, and they have a professional videographer accompany each dive and offer a DVD of your experience.
I hope to encounter a wild whale shark on a dive someday, and I've barely missed seeing them on two occasions - one during a mass appearance of larval lobster krill in Bonaire earlier this year, and last year in Honduras. But a miss is as good as a mile.
Nevertheless, I have this controlled experience to remember, and they are as majestic and awesome as you can imagine!