Shark Week's about as close as most guys ever get to the beasts, except for those few daredevil divers who ironically can't watch Shark Week, because using a remote requires arms. Just kidding, they're more afraid of you than you are of them! For proof, check out Shark Divers.
Ready to sea-whisk you 20 hours away to an island 150 miles off the coast of Baja for "guaranteed" Great White swims, Divers is run by an adventure seeking dude who's braved everything from Australian crocodiles, to Peruvian landslides, to Kiwi cyclones, which unlike sharks, don't leave you alone when you poke them in the eye. Anchoring in the 100+ ft visibility-waters near volcanic Isla Guadalupe (the most active white shark spot in the world after that island off South Africa, and...somewhere else), divers'll descend in 4-5 person, 50sqft cages which are air-supplied via surface hoses (eliminating the need for bulky tanks), and've been newly revamped by removing multiple bars for greater visibility, and compacted to "prevent drag", the biggest one of which would be if they improperly removed those bars. Pricing has also just this season become all-inclusive, with the fee netting you necessities like Mexican dive permits/vessel accommodations/all equipment, and even-more-necessities like unlimited beer and wine (the hard stuff's BYOB), and gourmet eats including dishes like stuffed pork tenderloin w/ balsamic cranberry reduction and vessel-caught, sesame seed-crusted ahi w/ soy/wasabi dressing, and signature desserts like puff pastry stuffed with fresh berries, and a cake they'll bake for special occasions, like "I just emptied my bank account to go shark diving".
If you prefer to be food, they've also just built a non-caged "cinema platform" for more advanced divers/photographers/death-wishers, which's lowered 40ft into the deep blue sea with absolutely no protection for the diver...though it's not like you'd be able to hold on to it for long anyway.
Photo by Jim Cornfield