As loathful as some of their actions in the war were, the Waffen SS can nonetheless be considered an elite force, seeing as their training, physical fitness & equipment placed them very high on the battlefield effeciency list compared to most foreign army units.
In the beginning the Wehrmacht didn't think much of the Waffen SS however, and rightfully so, seeing as the regular Waffen SS soldier hadn't undergone the rigorous training of the common wehrmacht soldier, which during that period (1935-42) had to undergo the longest & toughest basic training demanded by any military in the world, spanning over 18 months.
As the war went on however the Waffen SS began implementing more rigorous training, and the physical fitness was most likely the highest seen within any major army unit. Some of the demands were pretty outrageous.
Still, the soldiers of the Waffen SS weren't the absolute best trained soldiers of the war, that honor belongs to the specialist troops, which most of the major nations involved had their own versions of.
The specialist military units that recieved probably the toughest & best training during the war were the following:
LRDG (UK)
Brandenburgers (GER)
SAS (UK)
Fallschirmjaegers (GER)
Royal Marine Commandos (UK)
1st SSF (US & CA)
Gebirgsjaegers (GER)
SBS (UK)
502nd SS J