As Swedish, Danish, Norwegian and Finnish use several letters with umlauts, it is important to remember to use them in the correct way. Much hilarity or embarrassment might ensue if missed or used wrong. Some examples of Swedish words, where the meaning of the words is drastically changed due to the umlaut or absence thereof:
Låt - Lat (Tune - Lazy)
Låda - Lada (Box - Barn)
Kål - Kal (Cabbage - Bare)
Döv - Dov (Deaf - Muted)
Lök - Lok (Onion - Engine [for pulling trains])
Höra - Hora (Hear - Whore)
Säll - Såll (Blissful - Sieve; "Sall" isn't a word in Swedish)
Säl - Sal (Seal [animal] - Hall [big room])
Täcka - Tacka (Cover up - Expressing thanks [also ewe])
...you get the idea. In the 1980's, there was a British heavy metal band which called itself "Trojan". They wanted to be cool like Mötley Crüe and Blue Öyster Cult, and put an umlaut over the "o", turning their name into "Tröjan". They didn't really catch on in Sweden, as the name translated to "the sweater"...
Also, over a century ago, most of the safety matches were made in Sweden (more exactly in the town where I was born). Pirated copies of the matches sprung up, though, and the Swedish instructions on the box:
"Tända endast mot lådans plån" ("[Do] only light [strike] against the striking surface of the box") was also copied, but without the umlauts, turning it into "Serrate against the plain of the barn"...
I'm sure our Scandinavian friends here can supply you with examples in the other languages.