The Dude likes to drink White Russians, which is a drink made of Vodka, Kahlua, and Cream. The first time we see the Dude he's buying cream at Ralph's, which he pays for by personalized cheque (the background of the cheque appears to be a watercolor painting of a Blue Whale). At Maude's studio, The Dude can be seen using a powdered creamer in substitute of the cream.
At Jackie Treehorn's house, The Dude calls the drink a Caucasian when he starts to feel the effects of the sedative put in his drink.