Not only is that price incredible, but so is the choice. We searched random dates from January through March, 2014 and found these prices for itineraries as diverse as Salt Lake City - Copenhagen ($675), Detroit - Amsterdam ($678), Seattle - Madrid ($659), Minneapolis - Paris ($711), Milwaukee - Milan ($697). Simply search United.com and keep your dates flexible.
This is an unadvertised sale and the prices may disappear at any moment, so think fast. If you need a little extra time to think about, United does offer a "FareLock" option which allowed you hold the price for 3 days at a cost of $6.99, or 7 days for $8.99.
See you in Europe next spring!