Only milk from kosher animals, for example cows, sheep and goats, is kosher. Milk from non-kosher animals such as pigs or camels is not kosher. All milk looks the same and in former times it was the custom of farmers to mix milk from different animals. The rabbis, therefore decided that milk from a non-Jewish farmer is not kosher, unless a Jew observes the milking (Talmud Avodah Zarah 35b). This is cited as the authoritative halachah in the Shulchan Aruch (Orach Chayim, 115:1).
The situation has changed in the era of modern, industrialised farming and food regulation. With government supervision of milk production and penalties for misrepresentation, it is reasonable to trust the label that says "100-per-cent cows' milk". Rav Moshe Feinstein, the leading 20th-century halachic authority, ruled that on this basis one may drink unsupervised milk in the United Sates (and, by extension, other Western countries). Some still only drink supervised milk (chalav Yisrael) to be sure.