Hobbit mentioned the first ones that came into my head (Final Countdown, Axel F, Tubular Bells, Take On Me).
A few other ground breaking ones:
Telstar (1962) - The Tornados (aka Joe Meek) - Not my favourite, but one of the early popular synth lines, used a Clavioline.
Popcorn (1969) - Gershon Kingsley, the original, before Hot Butter got hold of it (using a MiniMoog amongst others, great production and use of technology for its era, can grab you by the bollocks even now - with its filter envelopes, delay + verb, and the offbeat hi-hat and kick, it's effectively trance some 30 odd years before it became mainstream [and the fucking crazy frog covered it])
I Feel Love (1977) - Donna Summers (iconic Moog modular arpeggiating, effectively kicking off the start of club music)
BladeRunner (1982) - Vangelis
Guess I'm a sucker for arps/gate/step-seqs, inc. AirWolf theme tune, Crockett's Theme (Jan Hammer), Blue Monday (New Order), Living on Video (Trans-X), Kids in America (Kim Wilde), Radio Ga Ga (Queen), et al.
Loads of New Romantic tunes of the 80's used synths, with Human League, Spandau Ballet et al, but Fade to Grey by Visage stuck out for me...
Fade to Grey - Visage
Are Friends Electric - Tubeway Army (Gary Numan)
Eurythmics - Sweet Dreams
Not specifically a synth, but a keyboard (organ) riff, the opening to the Phantom of the Opera:-
Bit of a 90's melodic dance kid so almost every synth riff seems iconic...
Anything from Hardfloor Acperience 303, although preferred Josh Wink's later Higher State of Consciousness
Prodigy - Voodoo People (2:42)
Underworld - Rez
...through to Energy 52 - Cafe del Mar
Faithless pizzi (JD990) Insomnia
& Salva Mea
Zombie Nation - Kernkraft 400
(C64 SID chip)
.. and beyond. Far too many to mention!