Direct information from my Biology of Sharks class:
We actually know quite a lot about Megalodon's life history from the fossil record. We know that it was a migratory shark which followed the migrations of the great whales of the time. Much like the modern day lemon shark, it traveled into shallow coastal waters around Florida, the Gulf of Mexico, the Carribean, etc. in order to give birth to its pups. Those pups stayed in the shallows and fed primarily on fish until they were around 7 meters long at which point they would travel out to sea and begin hunting whales.
One of the major hotspots for Megalodon was the area between North and South America- Megalodon was around before the two became connected by Panama. Whales would migrate through this fairly narrow area and the sharks would be waiting for them there.
Based on this information, I can confidently say that it is highly, highly unlikely that Megalodon still exists. Why? Well, a few reasons. First off, the whales that Megalodon hunted got bigger, and therefore much more difficult to hunt. A 60 foot shark is gonna have a hard time with an 80 foot whale. The isthmus of Panama also closed off, dramatically changing the migration routes of the whales. The sharks may not have been able to keep up with the new, changing migration routes of the whales after adapting for so long to the strategy of hunting around Panama. They may have begun to be outcompeted by smaller group hunting toothed whales. And finally, if Megalodon were still around, surely we would have seen one by now, as their migrations took them into shallow coastal seas to give birth so we'd be seeing both adult and juvenile megalodons regularly.
I hear many people suggest that Megalodon simply adapted to live in the deep sea, but there are some major problems with this "theory". Firstly, it would be a dramatic, drastic shift in behavior for the sharks; especially for a shark with presumably no deep-sea adaptations. Yes, coelocanths were thought extinct until discovered in deep water in the last century, but coelocanths have always lived in deep water habitats. Megalodons have always been coastal sharks and there is no evidence to suggest this fact changing. 2nd, the deep sea just would not support a shark of that size and nature. Sure, the deep sea supports some big animals, but megalodon was a lamnid shark who likely had an advanced thermoregulation mechanism (as many modern pelagic sharks do) as well as other advanced features that would require a caloric intake that would likely be too difficult to achieve as a deep sea predator. Just look at another massive deep sea shark, the greenland shark- it eats sleeping seals in the arctic but still doesn't have enough energy to go more than a few kilometers an hour- let alone achieve advanced thermoregulation.
Sorry guys, Megalodon is awesome, but I'm near-positive they're extinct.