Fly on Air Canada or United from Atlanta, Detroit, Minneapolis, or Seattle to Madrid for $395 roundtrip. This fare only includes carry-on bags, since United started charging extra for first checked bag to Europe recently.
As an example, I found seats departing Minneapolis MSP on Wednesday, October 17, returning from Madrid MAD on Saturday, October 27.
You'll find other dates for departures from the USA from September 16 through January 8, excluding peak holiday travel in Decemeber. A 7-night minimum stay is required and there is a maximum allowed stay of 1-month for this fare. Price may vary slightly depending on your routing.
These fares are unadvertised and prices may jump at any time. Book quickly to secure a low fare.
If you plan to check bags, you'll most likely want to purchase the classic economy fare, which I found to be $484 roundtrip for the above dates. This is less than what you'd pay in checked bag fees, which are now $60 each way on United/Air Canada's lowest fares to Europe.
If you're able to travel light and just take carry-on luggage, take advantage of these sub-$400 roundtrip fares to Europe. Other restrictions apply such as no ability to make changes and there is also a fee to select a specific seat. However, you are not required to choose a seat and can be assigned a seat for free at check-in. Consider these restrictions when choosing which fare is best for you.
Need a hotel in Madrid? Here's what's available for the above dates on Hotelwatchdog.