I am a US citizen with a valid passport. I am traveling to Norway via Amsterdam. I will have a long layover in Amsterdam and would like to leave the airport. Can I do so without a visa? If I need a visa, what kind?
Amsterdam is in the Schengen area, and as a US citizen you can enter the Schengen area for short visits (of up to 90 days of any 180) without having a visa.
This is the same rule that allows you to go to Norway without a visa, as Norway is also in the Schengen area.
(In fact, no matter whether you leave the airport or not, you will pass through the common Schengen immigration point in Amsterdam, and will not pass through immigration when you arrive in Norway).