SOMEONE ASKED THIS QUESTION ON QUORA SEE WHAT REPLY HE GOT :D
I would do nothing. Don’t sign into whatever account it’s in either. In other words, forget it and the account it’s in exists - for now.
Here’s why: First, because it’s incredibly unlikely that someone accidentally transferred $750k of their own BC to you. A purchase of goods in that amount is unlikely, and even less likely (to the point of “damn near impossible”) is making a mistake with the destination address.
In fact, I can think of only one semi-plausible scenario where that much BC might have been transferred to you: a hacker who had accumulated a bunch of stolen Bitcoin was trying to move/consolidate it, and mistakenly copied/pasted a destination address from his list of (stolen) addresses in place of his own. And the one he pasted happened to be yours.
That means (1) your address is on a list of stolen information, and (2) you just received stolen property.
So I definitely wouldn’t return it, because if you do that, the thief wins. But I also wouldn’t turn it over to the government, because the most likely scenario is that it’s a foreign hacker who they would have no ability to identify or pursue anyway.
Obviously the thief is never going to report it stolen, and it’s probable that it wasn’t stolen recently either - most likely it’s an accumulation of smaller amounts of BC that were lost way back in the Mt Gox hack, which means nobody is looking for it.
The US government considers Bitcoin property, not currency, and the statute of limitations of felony receipt of stolen property is three years. However, if you haven’t even logged into that account in three years then it’s entirely possible you didn’t know it was there, clearly weren’t a party to the theft, and didn’t even know that, how, or why it landed with you. But if you transfer it or cash out now, you’re on the record.
Most likely, there will be no investigation and nobody is looking for it. If three years pass and it’s still showing in your wallet, do whatever you like. If you decide to cash out after three years have passed, declare it as income, pay the taxes on it, and enjoy the windfall.