Yes, even with things they are "supposed to do" like cleaning their room and doing well in school. 

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Think about it, you applied for a job and you are doing what you were hired to do. But, it is still necessary for them to express appreciation or they lose employees who do not feel appreciated for the work they are doing. 

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By rewarding positive accomplishments, both big and small, you reinforce those accomplishments, they will want to continue (this is a good thing and means they are on track in development of understanding positive and negative consequences). 

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The more you reward positive behaviors, the more you will see positive and less negative. We all love hearing that someone we love is proud of us, or that they recognize our hard work, it feels good to hear that no matter what age we are so we shouldn't deny children that feeling.