If the collection is worth more than $10,000 you have to report it.
Three categories of coins are blocked from entry into the US, under various different laws and regulations.
The
Hobby Protection Act prohibits import of fake coins that do not have COPY stamped on them. If all your coins are genuine and/or all your fakes are compliant, no worries there.
Thanks to signed Memoranda of Understanding between US Customs and certain countries - specifically,
Cyprus, China and
Italy - ancient and mediaeval coins can in theory be seized and repatriated by US Customs if you cannot prove that they were taken out of those countries legally. And if you're a typical coin collector, you will not have such proof; a receipt from a coin dealer in Britain will not be good enough. But if all you have is modern coins, again, no worries there.
Bullion coins from certain "blacklisted" countries with which the American government has a dispute. Cuba, Iran and Sudan are the countries currently in the bad books; Burma was also until very recently. Depending on how the Ukraine Crisis resolves itself, Russia might soon find itself on the list too. How North Korea managed to negotiate their way off that list escapes me.
US Customs website. Circulation and collector coins are perfectly legal, despite
ebay's blanket ban on the sale of such items.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis