United has responded to Delta's nationwide sale to Europe with a little sale of their own. Amsterdam, Italy, and France are all in the mid $400s from nearly everywhere in the USA.
This is unadvertised and may not last very long. Book quickly if something catches your eye. Most third party booking sites have a 24-hour free cancellation policy so you'll have a day to figure out the details.
Travel is available on a wide range of dates, but generally through mid-May and from mid-September onward. For the most part, a 28-day advance purchase and a 7-night minimum stay is required. Some flights may be operated by Star Alliance partner airlines.
Fares include:
Charlotte to Amsterdam $454 round-trip
Atlanta to Amsterdam $456 round-trip
Hartford to Amsterdam $456 round-trip
Miami to Amsterdam $456 round-trip
Salt Lake City to Amsterdam $456 round-trip
Cleveland to Milan $464 round-trip
Orlando to Milan $464 round-trip
St. Louis to Milan $464 round-trip
Detroit to Milan $464 round-trip
Seattle to Milan $464 round-trip
Boston to Rome $481 round-trip
Austin to Rome $481 round-trip
Minneapolis to Rome $481 round-trip
Phoenix to Rome $481 round-trip
Portland to Rome $481 round-trip
Nashville to Paris $488 round-trip
Kansas City to Paris $488 round-trip
Raleigh to Paris $488 round-trip
San Diego to Paris $492 round-trip
Honolulu to Paris $508 round-trip
As this is pretty much nationwide, check flights from your city, within the travel dates listed above, to see what's available from your area. Unfortunately, most United and American hub cities are excluded.
Generally, prices are in the mid-to-high $400s round-trip from nearly everywhere in the USA to Amsterdam, Paris, Rome, Milan, Venice, Lyon, etc. Even if your favorite airport (small or large) isn't listed, there may be a big price drop. Other cities in these countries are likely lower than normal as well.