In what is known as the over-justification effect, an explicit extrinsic incentive can actually decrease the motivation to perform the given task. For example, if one was a web developer and proposed to build their friend a website as a gift of sorts, a fiscal offer under market value would sour the desire to build the website. Alternatively the friend could allow the favour to be completed altruistically and then follow up with a meal at a restaurant.
An even better example relates to intrinsic vs. extrinsic motication.