The greatest engine of all time has to be the SR-71A Blackbird's Pratt and Whitney J-58 axial-flow turbojets. Known to propell that spy plane to over Mach 3 it is rumoured to have gone a lot faster. But you could also pick the Apollo programme's Saturn V first-stage Rocketdyne F-1 engines.
I saw the SR-71 fly at Farnborough years ago. It was the loudest aircraft i've ever heard.