Note: Answers appear in the comments.
Answers:
1. Slide the newspaper half way under a closed door and ask the two people to stand on the bit of newspaper on their side of the door.
2. There are twelve (not four).
3. Actually, the ladder will rise with the ship!
4. Dimes are smaller than nickels, so choose the dimes!
5. If they put them all together, there will be one pile.
6. Horse racing.
7. The President.
8. Throw the ball straight up.
9. Suicide
10. Sleeplessness