The flower forget-me-not is named "Vergissmeinnicht" in German and "Незабудка" in Russian. The meaning is the same in all three languages. Is this a coincidence?
I tried to come up with a motivation for why this might be a loan word instead of something that people would come up with a suitable native word for. It's tempting to just say, "well that is the way it is, end of story" Here are my ideas
1 It's easy to translate/calque as a phrase. There isn't anything awkward about it and in English it forms a complete sentence. Compare this to Chinese loans to English-- they are few and become unrecognizable.
2 Plants have limited ranges, so who ever lives near that plant will likely name it first and the name would spread with the knowledge that the plant exists. As it turns out for this plant, it has a wide range, so it is possible that in some places the locals had already come up with a word for it. On the other hand, something like words banana and tea are likely to have traveled with the people who first named these plants. In the case of Tea, WALS has lots of data on how the name of that plant and the loanwords spread.
As @Mitch pointed out in his comment, there is a phenomenon called calque or loan translation, where a word or a phrase is borrowed by word-per-word (or root-per-root) translation. According to the Online Etymology Dictionary, that's what happened here
from O.Fr. ne m'oubliez mye; in 15c. the flower was supposed to ensure that those wearing it should never be forgotten by their lovers. Similar loan-translations took the name into other languages, cf. Ger. Vergißmeinnicht, Swed. forgätmigej, Hungarian nefelejcs, Czech nezabudka.
Like many flowers, the Forget-me-not is named for its color. For unbelievable folk-etymologies, see http://symbolism.wikia.com/wiki/Forget-Me-Not
A Google image search indicates that the color of this flower ranges from light blue to red-violet. The most common Hebrew word for purple is SeGoL סָגוֹל. In second place, it is @aRGaMoN אַרגָמָן, probably borrowed from Akkadian argamannu.
In many Hebrew nouns, the aleph which had been at the end of the word (but had lost its ancient northern GHT-sound) moved to the beginning of the word under the influence of Aramaic which used aleph as a suffix for the definite article. So moving the aleph in @aRGaMoN אַרגָמָן back to its original location makes the German name for this flower an excellent phono-semantic match for that Hebrew color.
aRGa Ma Ni[GHT] VeRGissMeinNiCHT FoRGet Me NoT
The German name was translated to French ne m'oubliez pas. The English name may have been independently transliterated from Hebrew or translated from French or German. Compare Yiddish Fargesnitl. Wikipedia thinks the English name was calqued from French.