Combine milk, rice, sugar, raisins and salt in medium saucepan. Bring to a boil, stirring constantly. Reduce heat to medium-low; simmer 6 minutes, stirring occasionally.
Beat eggs and vanilla lightly in a small bowl. Stir small amount of hot mixture into eggs. Stirring constantly, slowly pour egg mixture back into hot mixture. Stirring constantly, cook on low heat 1 minute until thickened. Do not boil.
Remove from heat. Let stand 30 minutes; serve warm. Store any remaining pudding in refrigerator.