I think the current usual solution is to get a debit card (or failing that a credit card) with low/no foreign transaction and cash withdrawlwithdrawal fees. (In the UK, the Halifax Clarity Card is the best for this at the moment)
Then, when you get to the country, take out cash periodically. Not too much in case of issues, but don't assume you can do it too often as you may not always be able to find a cash machine depending on where you are.
It's worth getting a little bit of currency before you go (if you don't have it left over from another trip), so you can buy a coffee while you wait for everyone who got off the plane quicker than you to finish using the cash machine at the port/airport/station!
Edit: Since you've said you're in the US, I can't suggest the best card for you to get to avoid/minimise foreign transaction fees, but asking on the personal finance SE site is likely the best bet for finding out what that card is.