While we're on Dexy's, the intro to Jackie Wilson Said (I'm in Heaven...) is brilliant, especially when the alto sax kicks in. Better than Van Morrison's original simply for the quality of the recording.
A few other suggestions, based on it being intros.
Europe”The Final Countdown” - cheesemungous but impossible to hear and not dream of being a Scandi bubble-permed astronaut.
Prince “Let’s Go Crazy”. I can already think of a few other shouts when you contemplate his back catalogue.
U2. “Sunday Bloody Sunday”. It is a short intro but so visceral.
Jimi Hendrix - I think “All Along the Watchtower” has been rightly mentioned. “Hey Joe” and “Voodoo Chile” need to be in there too. Hendrix was a fantastic guitarist but his bassist and drummer are probably not given the credit they deserve. The intros to all those tracks are just accomplished, they sound loose but are actually super-tight, musicians on the top of their game working perfectly with each other.
I will slip in a personal favourite or two. I love the intro to “I Believe” by R.E.M., love the whole song TBH, this was just before they became really famous and were still more student-indie than MTV. It was on their album ‘Document’ IIRC, which was followed by ‘Green’ which had ‘Orange Crush’ and other hits and the next album had ‘Losing my Religion’ and they went stratospheric.
And in a complete change of tack, the intros of ‘Chime’ and ‘Belfast’ by Orbital. Hearing the opening notes of either of those takes me to a happy place
There's only one thing better than a Hibs calendar and that's two Hibs calendars
There's a YouTube series on the best guitar/bass/piano etc intros of all time. It's a bit heavy on "rawk" IMO, but it's good fun.
That guy does great break downs on why certain songs are so good, goes into the way they are recorded and the instruments etc, it's fascinating to see someone who knows what they are talking about go into it all