A few have already answered with a Hard Days Night, which I think is prefect. Straight to the point, short and sweet, instantly recognisable. Another fav of mine is Five Years- Bowie, that drum beat unmistakably Mr Bowie and a great track as well.
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Perfect in a way- except with A Hard Day’s Night, it isn’t actually an intro at all, but straight in with the song itself…
… with a small but perfectly formed intro. 
“At first I was afraid, I was petrified…”
G
Money for Nothing, surely! Just listen to the crowd’s response when played live:
Mark
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Not sure which is best, but a one note starter must be Lou Reed And Walk on the Wild Side.
Others -
Bob Marley - No Woman, No Cry
Cowboy Junkies - Walking After Midnight
Aaron Copland - Fanfare For The Common Man
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Pretty Vacant - Sex Pistols
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That first G major chord and it’s instantly recognized as Wish You Were Here!
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Except on the original (studio) version, that guitar riff doesn’t occur until 1:36 into the track!
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You could try telling that to the audience on the Live version I posted, but I doubt they’d hear you!
D1ck Dale - Miserlou
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Besides all the great suggestions above: 7 Nation Army
Owner of a Lonely Heart by Yes and Another Girl Another Planet are both pretty distinctive.
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The Only Ones! Good call.
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Jessica by the Almond Brothers - ingrained from watching Top Gear!
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Played this again last night, and what I consider to be the intro actually lasts well over 3 minutes! You might argue that it doesn’t really count as an intro, but for me, the way it gradually builds, before letting loose, is one of the most memorable intros.
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The Breeders - Cannonball
For any F1 fan it surely must be Fleetwood Mac’s ‘The Chain’? Like many of the above, recognisable from the first chord.
Big Eyed Beans From Venus by Captain Beefheart and the Magic Band:
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Good call!