Ever wonder what's so funny to your child as she flicks the switch and gets the elephant to appear on her pop-n-see? It's not the funny sound or even the sudden appearance of the "effelant"; It's simple cause and effect. She caused the elephant to appear and that makes her happy. Children are happiest when they can exercise some control over their surroundings (think about it: you don't like being told what to do, so why should they?). Giving your child simple options and allowing him to make decisions is a great way to let them be in control of their lives - partially at least. This is a small step towards independence, gaining self confidence, learning self reliance and strengthening the parent-child bond.
I'm not recommending you let your 3 year old do whatever he wants. However, letting him choose between wearing the blue pirate shirt or the green dinosaur shirt, helps him to begin to identify what he wants and why. This simple action goes a long way in building his identity. He is also more likely to show an interest in getting dressed (which is helpful if you have a little streaker at home) if he's included in the process. He'll feel more confident, a strong sense of pride, and a smidgen of respect for you, for allowing him the freedom to choose. And don't stress things that don't really matter. Give them free range over things that you're not going to be a stickler about. Which book they read at bed time is far less important than the fact that they are reading. So if they want to read Good Morning, Sun at 9pm, read it!
Allowing children to make their own choices also helps teach them about consequences. Once your daughter decides on wearing the pink sneakers, she shouldn't be allowed to change her mind over and over again making everyone late for work and school. She was given the options and now she has to live with the pink sneakers for today. Constantly giving in to children shows them that your boundaries are meaningless and they begin to lose respect for you as an authority figure. So hold firm to your limits. If the options are broccoli or carrots with dinner and they ask for corn for the third night in a row, gently explain that "We had corn yesterday, today we can have broccoli or carrots. We can have corn again on Thursday."
The key to letting your kids make choices is being comfortable with all the options you give them. Don't give her options that you don't approve of, that will upset you, or if you're not going to be supportive of her decision. Just because you think the yellow rain coat looks cuter, doesn't mean she's wrong for choosing the red one. Respect the fact that she likes the red coat and feels more comfortable and confident wearing it. So make sure their options are age appropriate and parent approved, and then leave the decision making to them.