Combine milk, sugar and rice in a heavy saucepan. Bring to a gentle boil over medium heat, reduce heat to simmer and cook uncovered for 1 hour, stirring occasionally. (The milk should just barely simmer, with bubbles breaking only at the outside edge of the surface. After an hour, the rice should be soft.)
Add raisins, increase heat to medium, cook, stirring frequently now, until rice has absorbed most of the rest of the milk - - but not all - - and the pudding is creamy, about 30 minutes longer.
Remove from heat and stir in the vanilla. When cool, it will thicken, but still be very creamy - - with no cream. Serve warm or well chilled.
Here are some tasty variations to this "classic rice pudding" recipe ...
A Thai-Pudding Delight - substitute a 14 ounce can of coconut milk (not cream of coconut) for part of the milk. Fold in 1 tablespoon zest of lime and garnish with lime zest and shredded toasted coconut.
Mocha Rice Pudding - add 2 teaspoons instant espresso powder when adding vanilla extract. To cooled pudding add whipped topping and sprinkle with a mixture of sugar and espresso powder.
Swedish Rice Pudding - to cooked and cooled Classic Creamy Rice Pudding, fold in 3/4 cup whipped cream. Add 1 teaspoon almond extract with vanilla extract. Top with toasted almond slivers.
Strawberry Parfait Rice Pudding - in four parfait glasses, alternate Classic Creamy Rice Pudding with layers of fresh strawberries. Top with whipped cream and a dollop of strawberry jam