To stick to the letter of the title.
Ancient: The Spartans in their prime, unsurpassed I think.
Mid millenium: The Janissaries, captured boys usually Christiian converted to Islam and trained to be the elite warriors of the Turks.
Napoleonic: The British army.
WW1: Toss up between the German and the British armies
WW2: Probably Das Reich as Hortlund says, or any Waffen SS but only mid war. Late in the war fanaticism made up for training. Same goes for any German formation. The Fallschirmjager were diluted by transfers of Luftwaffe personnel late in the war. in fact the paratroops of America, Britain were directly comparable and just as good.
Current: The Royal Marines, no contest.
Man for man though in fighting qualities, the Germans have it. I suspect that's still true even though they don't fight warsnowdays. It's a national characteristic. Let's not forget Israel, quite simply they have to be the best, their survival depends on it.
An of course, although I admit bias here, the Irish. Few are the wars where no Irishman or Irish unit served. Sometimes on both sides. We love trouble. In any squad size battle the Irish would win or get wiped out. LOL:D