When you are sitting at the table with someone, and there's a bottle of milk that you can't reach on the table, you will normally say:
Could you pass me the milk, please?
"Some milk" is possible grammatically, but why would you ask another person to pass you an unspecified amount of milk? I think it's a conceivable but uncommon question. "Any milk" is even stranger to me. In what situations do you just need milk, no matter at all how much?