When I was really young, I would often ask for the change that my parents got when they made purchases at stores. I would usually only add up to a few cents, but I would always save my money for bigger things later (I was surprisingly patient and organized for a child my age).
Later, in order to teach me responsibility, I would do simple chores around the house and got an allowance (about $5 or $10) a week. Again, it wasn't much, but I would always save my money and I would get a lot of great things over time.
Once I started high school, I would do chores around the house and I would no longer get an allowance. It didn't really bother me though; I would have a lot of money saved up, and I also did odd jobs on the weekends.