That depends. Are you asking about a legally issued coin? If not, the most expensive may be the US 1933 double eagle. It was legally minted but recalled before issuing and all but a few were destroyed. The only one which became available was sold as follows:
" The 1933 Double Eagle sold at auction on July 30, 2002, for $6.6 million, plus the 15% buyer's fee, which brought the total cost to the buyer to $7,590,000, plus $20 to monetize the coin and compensate the Mint for the $20 it believes it lost when the coin was thought to have been stolen."
However, it may not be the most valuable coin any more because 19 more turned up. They were seized by the Secret Service and their fate remains under litigation. If they are destroyed the remaining coin may be even more valuable. If they are released, the coins may decline in value somewhat.

If you are asking about a fully legal coin, the contender would be this:
"The only remaining 1609 centen coin, the biggest solid gold coin to be minted in Spain and considered to be the most expensive in the world, was sold at auction today in Barcelona for its reserve price of 800,000 euros."

Or, perhaps this (only an estimated value, not an auction price):
"1804 Bust Dollar
Estimated Value: $7,500,000
The 1804 Bust Dollar is considered one of the most famous US coins because of its rarity."

There are other coins that are considered priceless, because single examples exist only in museums