I fly out of Seattle. I have only redeemed miles to Europe once, SEA-JFK-FCO (Rome) last May on American, booked 3 months ahead. I also have miles on Delta, Continental/United, and US Airways. I did fly on Alaska in August using Delta miles.
Delta is hard to redeem on because the low level saver awards are hard to find, partly because of their 3 tier redemption chart. They may not release seats at the lowest level 330 days out, they may not release any later, either. I've had my eye on the Air France nonstop flight Seattle to Paris, but Air France releases seats only 10 months out and availability is sporadic during the summer. Delta and KLM fly nonstop to Amsterdam, but I have never seen this route available at less than 75,000 miles. Only the low level awards are available for booking on Alaska miles, and those can be hard to find. You can also redeem on Alitalia using Delta miles.
American is rumored to have the best availability, even to Europe, and they have coach seats available to Europe at only 40,000 miles off peak. AA miles are easy to get, see
this post. The downside is you have to connect in Chicago or New York, unless you pay the extremely high fuel surcharges to fly on BA SEA-LHR. AA miles are also excellent for traveling to South America on LAN.
I have not redeemed miles on a Star Alliance carrier yet (United, Continental, Us Airways). I like that there are multiple cards to earn bonuses on (Ultimate Rewards points from the Chase Sapphire and Ink Bold cards can be transferred to Continental miles, and rumor is United will be a transfer partner later). I also like that the US Airways Visa lets you redeem tickets to Europe for 5,000 less miles (in January and February you can book a coach ticket for 35,000 miles to Europe). Lufthansa is a partner, and they fly nonstop from Seattle to Frankfurt. I understand it is easier to redeem tickets on Continental than on United, so once Continental is gone it may be harder to get awards.
AA miles may be the easiest to accumulate and redeem as long as you don't mind connecting in Chicago or New York. But you can find nonstop flights to Europe with Delta and United miles, even if you make a connection in Europe you'll save on travel time.