This thread is about exactly what the title says.
For me, it's:
George "Shadow" Morton (The Shangri-Las, Vanilla Fudge, New York Dolls, Mott the Hoople)
Ray Manzarek (Echo and the Bunnymen, X)
Flood (Depeche Mode, Erasure, Nine Inch Nails, Nick Cave, Pop Will Eat Itself, Nitzer Ebb, Curve, Smashing Pumpkins...)
Al Kooper (The Tubes, Skynyrd)
Bob Ezrin (Everyone - like, I'm not kidding, look up his resume on wikipedia)
Ric Ocasek (Suicide, No Doubt, Weezer, Bad Brains)
Daniel Miller (Depeche Mode, Silicon Teens, many Mute Records acts)
Eric Radcliffe (Depeche Mode, Yaz, Fad Gadget)
Brian Eno (Also everyone)
Sam Phillips (Elvis)
Martin Hannett (Joy Division, Durutti Column)
Tony Visconti (David Bowie)
And, if self-producers can be counted, Bauhaus and Trent Reznor.