The short answer
Plenty. Mint tea, green tea brewed with fresh spearmint and sugar, is served everywhere. Fresh orange juice is squeezed to order at the Jemaa el-Fnaa carts. Cafés serve nus-nus, half coffee and half milk, and there are specialist tea and coffee houses in the medina. Most of Marrakech's daily life runs on these drinks.
In more detail
Mint tea, atay, is the thread through every day: in shops, homes, cafés and carpet showrooms. It is Chinese gunpowder green tea brewed with a fistful of fresh spearmint and a lot of sugar, poured from about 30 to 45 centimetres above the glass to raise a crown of foam, usually in three rounds from the same leaves. Drinking a glass in a shop does not oblige you to buy. Hold the hot glass by the rim and base.
The orange-juice carts of Jemaa el-Fnaa squeeze to order from the morning. In cafés, regulars order nus-nus, meaning half and half, a coffee cut with milk; Cafe Les Negociants in Gueliz has served it since 1936.
For something more particular, 1112 Tea House in the medina pours teas from twelve Moroccan regions, including a rose-petal Draa-Tafilalet blend. The tea salon of the Moroccan Culinary Arts Museum, next to the Bahia Palace, serves Moroccan teas in a restored palace. Bacha Coffee in Dar El Bacha offers more than 200 Arabica coffees.
In Ramadan, the fast breaks with dates and milk or water before the harira, which is a good reminder that milk drinks are part of the Moroccan table too.