I know that in German language, there are three noun genders, der, die, and das. All three of these words mean "the": der being masculine, die being feminine, das being neuter.
Those are actually the definite articles, not the nouns themselves. Gender is also indicated in the form of the nouns, but not clearly. The inflections (suffixes) that mark grammatical case (nominative, genitive, dative, accusative) vary according to gender. In the masculine singular:
der Mann, des Mannes, dem Manne, den Mann.
In some of the Romance languages (descendants of Latin) gender is more clearly evident in the noun. In Spanish, Portuguese and Italian, most (but by no means all) masculine nouns end in
-o and feminine nouns in
-a. (There's no neuter gender; Latin had one but it's been lost.) Prominent exceptions are glaring, such as Spanish/Portuguese
el hombre/o homem, "man" and
la mujer/a mulher, "woman."
Inflections for gender are often also required in associated adjectives.
El hombre gordo/la mujer gorda, "the fat man/the fat woman."
Do all other languages have genders like this? Is English unique in that it does not?
Gender was a paradigm in the Proto-Indo-European language, so many of its descendants still have it. The grammatical complexities that go along with it have been simplified to varying degrees in the individual Indo-European languages.
It's not quite correct to say that English does not have genders, since we retain it in our third-person pronouns: he/she/it; and at that it's only in the singular pronouns: there is only one word for "they." Nonetheless, gender in English is not a grammatical construct but a desciption of the biological gender of the pronoun's referent... yeah well except for the fact that we call ships "she."

Chinese, one of myriad non-Indo-European languages, literally has no genders: there is only one third-person pronoun,
ta, which means he, she and it.
Afrikaans, Bengali and Farsi are three more Indo-European languages that are essentially devoid of gender like English. The Scandinavian languages are not far behind; in Danish, Norwegian and Swedish inflections for gender are not common. (Sorry, I don't know about Icelandic, which often retains older, more conservative forms in both grammar and pronunciation.) The Slavic languages, on the other hand, are rife with inflections for gender in both nouns and adjectives--as well as for case.
There are dozens, perhaps hundreds, of other language families such as Finno-Ugric (Finnish, Hungarian, etc.), Mongolic (Turkish, Uzbek, Mongolian, etc.), Malayo-Polynesian (Hawaiian, Maori, Tagalog, etc.), Athabascan (Navajo, Tlingit etc.), Afro-Asiatic (Hebrew, Arabic, Ancient Egyptian, Amharic, etc.), Niger-Congo, Bantu, and whole troves of them in Africa, Australia and central Asia, some of which have eluded categorization. Of these, the Afro-Asiatic languages have a gender paradigm that would be familiar to us. This introduces the concept of a
Sprachbund, a group of languages that are not related by ancestry, but whose speakers have interacted with each other for so long that they have assimilated some of each other's language characteristics such as phonemes and grammar. (I don't know if this is specifically the case with the Indo-European and Afro-Asiatic families' sharing of grammatical gender, but the speakers have been in close contact for millennia and three of the world's six civilizations arose in their homelands.)
But study of these (to us) extremely "foreign" languages reveals that
gender is only one type of categorization system of
noun classes.
- The Algonquian languages such as Ojibwe distinguish grammatically between animate and inanimate classes of nouns. The general pattern is that living things, sacred things, things connected to the earth, etc. have power and are animate, while other things are not. Nonetheless its paradigm has broken down so that raspberries are animate while strawberries are inanimate.
- The Athabascan languages distinguish nouns according to animacy but also shape and consistency. However, these languages do not express the noun class in the noun itself, but in the verbs.
- Some noun class paradigms are completely inscrutable. The Dyirbal language of Australia has four noun classes: animate objects and men; women, water, fire and violence; edible fruits and vegetables; everything else.
- Fula, a Niger-Congo language, has 26 noun classes (a count that varies by dialect). Other languages in this family have noun classes such as one for objects that come in pairs or groups rather than singly, for general versus precise locations, and various abstract qualities.