Like every good amateur historian, I know that Vikings never wore horned helmets because they represented a danger to the wearer. However, is the same true for these helmets? If the Teutonic Order never wore them, where did the myth come from? And if they did, why didn't they worry about the same things as the Vikings?
Such crests were certainly in use for ceremonial and heraldic purposes by the elite (i.e. tournaments/funerary/etc.). For example, the pages from the early 14th centry Codex Manesse depicts a few. The latter image does not depict a Teutonic Knight, but nonetheless indicates the fashion of the times, and helmet choice for members of the order was up to personal preference; there were no uniform rules in this respect.
However, it is not likely that helms with such massive crests were used in battle due to practical concerns, though this is supposition.
Check out this more in depth answer to your question by /u/Gaimar.
Short answer: Probably not.
Long answer:
Origin of the myth:
The myth of the Teutonic Knights with horned helmets spawns from the soviet 1938 movie, Sergei Eisenstein's "Aleksandr Nevskij", which arguably features the most famous representation of Teutonic Knights in pop culture. Now, where did Eisenstein took inspiration? Most probably from the miniatures of the german Manesse Codex (1300 AD ca.), arguably one of the most famous german contemporary visual source for the Middle Ages and incidentally, one of the most famous in general. The miniature represents German minnesanger (trobadours) and knights, but the only mention to the teutonic knights is in the portrait of Tannhauser, which is wearing a white robe with a black cross.
So, did the Teutonic Knights actually wear horned or decorated helmets?
The Teutonic Order was a military order; that is to say, its members were warrior-monks. Their rule had strict regulations on the dress code. They could not bear their personal coat of arms (many had one before) but only the order's black cross on silver as their coat of arms. No form of decorations was allowed, because that would have been against humility and modesty. It may be interesting to know that the "black", in Heraldry, STOOD for "Humility". So, according to the rule, they were not allowed to wear those fancy helmets and the answer would be NO.
That said, who knows if someone broke the rule or decorations were actually tolerated? Can we be sure that exceptions weren't made and everybody followed the rule strictly?
About horned and decorated helmets in general:
In general, it can be argued that those fancy decorations weren't actually used in the battle but more so in tournaments and in other more elegant occasions, simply because those were fragile decorations and why would you risk to ruin them? This reinforce the idea that the Teutonic Knights probably never wore those.
As for the vikings, the Viking horned helmets are indeed a 19th century myth. Nothing suggests that the Vikings actually wore horned helmets at all and sure thing, Viking were not associated with horned helmets during the middle ages.