Many 2-year-olds assert their desire to take charge of a situation on a daily basis. "I can do it myself!" is an oft-repeated declaration. The parent of a toddler needs to give in to such demands as much as possible (but with an eye to safety, of course).
Letting a 2-year-old put his coat on by himself can take twice as long, and stepping aside to let him climb unaided into the car seat will slow down your departure. But allowing -- even encouraging -- such attempts can go a long way toward shaping your child's view of himself as someone who is a competent, separate person.
A toddler's ability to entertain himself builds confidence. (It's also a valuable lifelong skill.) Many parents underestimate how well a 2-year-old can keep himself occupied for short periods. You can help foster such skills in your toddler in several ways. First, during time together, be actively engaged with your child, not absentmindedly watching him with half an eye on the television. If he shows you a picture he's made, don't placate him with "That's nice," but point out specific parts of the drawing you like and ask questions about it.
Also, provide plenty of safe, simple toys that give your child's imagination free rein: blocks, pots and pans, a toy dish set, crayons and paper. You'll still want to be your child's "playmate," but try not to create an environment in which your child relies on you for constant entertainment and is incapable of entertaining himself.