A song is a relatively short musical composition for the human voice (possibly accompanied by other musical instruments), which features words (lyrics). The words are typically of a poetic, rhyming nature, although they may be religious verses or free prose. Songs can be broadly divided into many different forms, depending on the criteria used. A common division is between "art songs" and "folk songs", the latter being of anonymous origin and culturally associated. Other common methods of classification are by purpose (sacred vs secular), by style (dance, ballad, lieder, etc) or by time of origin (Renaissance, Contemporary, etc). The performer of a song is called a "singer" or "vocalist".
Art songs are songs created for performance in their own right, usually with piano accompaniment, although they can also have other types of accompaniment such as an orchestra or string quartet. Generally they are defined as having an identified author(s) and require serious voice-training. The German word for song, "Lied" (plural: "Lieder"), is used in French and English-speaking communities to refer to the serious art song, whereas in German-speaking communities the word used would be "Kunstlied" (plural: "Kunstlieder"). Art songs feature in many cultures, including but not limited to: Russian (romansy), Dutch (liedje), Italian (canzoni), French (mélodies), Scandinavian (sånger), Spanish (canciones).
Folk songs are songs of anonymous origin that are transmitted orally. They are frequently a major aspect of national or cultural identity. Art songs often become folk songs when people forget who the author was. Folk songs are also frequently transmitted nonorally, especially in the modern era.
At http://www.lieder.net/ you can find thousands of texts to classical art songs in many languages, with thousands of translations to English.
Song forms (haven't decided if these should be separate pages yet)
Aria and recitative (Opera)
Lied (plural: Lieder)
Gregorian Chant and plainsong
Rock and Pop songs
Ethnic or indigenous songs (a horrible term to use but I couldn't think of an alternative just yet. Aboriginal song is the only area I have any expertise on)