> Some

- Used to show an indefinite quantity (the exact number is not important) and in affirmative statements.

Example:
I have some books.
She wants some apples.

- Used in questions, but only when you think the answer will be 'Yes'.

Example:
Do you have some paper? (I hope the answer will be 'Yes')
Would you like some french fries? ( I expect the anwer will be 'Yes')

> Any

- Used in negative statements.

Example:
I don't have any money.
There aren't any taxis near here.

- Used in questions, especially when we expect the answer will be 'No'.

Example:
Do you have any paper? (I expect the answer will probably be 'No')
Is there any time to go to the doctor's? ( I think there probably isn't time).

> Notice

Some and any are often used like articles for plural nouns.

- A/an is used for singular countable nouns, and some/any can be used for plural noun, countable or uncountable.

Example:
I have a newspaper, some newspapers, and some money.

Beginners
English exercise "Some and any" created by anonyme (02-10-2005) with The test builder
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1. Fred is very busy : he doesn't have time.
2. Let's listen to music !
3. We need butter and bread for dinner.
4. Do you have pets ? (I think he doesn't have one)
5. Yes, I have !
6. Rachel meets friends at the weekend.
7. Do you have orange juice ? (I don't see it in the fridge)
8. No, I don't ! But I have grape fruit if you want !
9. Do you want ?
10. They went to town without money !