Scandinavian Airlines frequently sells seats on its own web site for less than you'll find them anywhere else. Right now they have several deals online.
One is discounts on their comfy "economy extra" class to Scandinavia. This service provides extra leg room and wider seats, business class check in and baggage allowance, fast track security, and a PC power outlet at all seats. How are the fares? Seattle to Helsinki for July travel, for example, you can find fares for $1710 RT with tax. That may sound like a lot, but keep in mind that many airlines are charging that for plain old economy. In fact, SAS itself is charging $2222 for plain old economy on some July dates, so clearly you're better off paying less for a better seat! It's very easy to pinpoint the days when fares are lowest on SAS's site.
In addition, SAS is offering business class discounts to Europe. Newark to Amsterdam, for example, is offered at $2500 RT; Seattle to Copenhagen at about $2800 RT.
Back in the back of the bus, you'll find good fares for travel through June 22 in SAS's economy class. For example, we found Newark to Copenhagen leaving June 8 and returning June 15 for $655 RT including taxes. We did find slightly lower fares ($621 RT) on those travel days on that route via United with a connection on SAS, but frankly we'd rather do SAS, since they leave Newark at 11 PM, which gives us the whole day and means we might actually fall asleep on the plane during the outbound trip.