Lol @ LORD_EC
I suppose I have to agree with Crook. At first I wanted to say the Sputnik launch by the USSR (Russia) was the greatest, but after weighing that with a human landing on Moon, can't compare in terms of technical achievement
Rather, Sputnik's launch was more the most "significant" engineering achievement in the 20th century. It sparked the space age race, plus, it actually led to the creation of US's NASA!
Back to the landing of Moon.. it combined many different disciplines of engineering with their respective breakthroughs.
Mechanical: aeronautics, dynamics, statics, engines, rocket structure,
Chemical: rocket fuel, oxygen supply,
Material: space suits, rocket shielding/skin,
Electrical/Electronics: power supplies, life support systems, computers and most importantly, communications

... amongst others. It requires alot of effort!
Can't wait until we land a man on Mars

Maybe some of us Crazy Engineers will take part in it! haha