Combine rice, milk, sugar, and salt in a medium saucepan. Bring to a simmer over medium heat, stirring occasionally.
Reduce heat to low, cover, and simmer for 45-60 minutes, or until the rice is tender and the pudding has thickened, stirring occasionally to prevent sticking.
Remove from heat and stir in cinnamon and vanilla extract.
Serve warm or chilled.
Notes
For extra creaminess, use whole milk. You can also add raisins or other dried fruits for extra flavor.