New Order's "Blue Monday" is like the crown jewel of 1980s synth pop. I love that song, and the 1988 remix is nicely done.
And now I get to pull out some related trivia! Woohoo! First of all, here's a more recent synth pop song, called "Stiff Kittens" by Blaqk Audio. Blaqk Audio is the electronic side project of some of the members of the alt rock band AFI. "Stiff Kittens" is an obscure reference to the group Joy Division, which later became New Order. Anyhoo...
http://www.youtube.com/watch?v=locBlaxOChA
Excellent, excellent stuff. Davey Havok channels Dave Gahan (Depeche Mode) in Violator-era goodness here.
Speaking of remixes, the 1989 remix of Real Life's "Send Me an Angel" is better than the original, I think:
http://www.youtube.com/watch?v=0R6WIbx8ysE
And speaking of New Order, I must post my favorite of theirs, "Bizarre Love Triangle." Many remixes of this song, too. I chose this one because the top rated comment included "I hate Justin Bieber." Yes.
http://www.youtube.com/watch?v=fOWBX_xP5y8
Since this has now wandered into
good synth pop territory, I'll end with the always delightful but definitely odd "White Horse" by Laid Back.
http://www.youtube.com/watch?v=I8j2ej5jqQw