Another question has asked whether magic would be immune to science's scrutiny. I'd like to invert the question and ask...
Would science even exist in a world with magic?
Science evolves in an arena where the results of laboratory experiments can be consistently repeated. A theory gains acceptance as subsequent repetitions of a supporting experiment yield identical results. In the mundane world, it only takes a single experiment yielding a contrary result, to dispel all of a theory's credibility.
Repetition is the raw material which modern scientists use to incrementally span the chasm of our ignorance with every new discovery building up from the repeat-ability of all the experimental results upon which it stands.
Now for the sake of this question, lets imagine a pretty straight forward definition for magic: Magic is an invisible gas or energy (we don't know which). It cannot be proven to exist nor can it be detected by any known scientific method. Its singular affect is to temporarily change the nature of the universe from "Cause and Effect" to "Intent and Effect". In the presence of magic, the expectations of the most attuned mind override all other factors in determining the result. Magic ignores the need for causative forces, side-stepping the all known laws of conservation including energy, mass and sanity.
Magical results rely solely upon the presence of the magic whose only proof of presence is those same magical results. Independent and allusive, magic is impossible to build anything upon. By itself, it cannot span the chasm of our ignorance.
Mental attuning is the only theory we have so far, for uncovering the nature of magic and it is just a statistical shadow. It is believed that ... some people are present during magical effects more often than others and after the fact, those same people are more happy with results than a randomly selected sample of the other people present. We know that these people are magically favored over everyone else, but that is all we know about them.
So here is the question: In a world where this kind of magic existed, would science ever take root? What tools and techniques might magic-fearing scientists use to defend their experiments from magic?
Feel free to bend the definition of magic to suit your answer; after all, magic is malleable by definition.
-- EDIT 3/31/15 --
I failed to comment on how rare magic is in this world I am building. Several of the current answers have pointed out that if this magic was everywhere, then major aspects of everyday life (such as transportation systems) would never have been developed. Magic would relieve society of the need for such infrastructure.
I am trying for a subtler effect, where magic is rare, where an average person might only encounter an undeniably magical event once or twice in a year. A very attuned person may cause a small event or two in a good week, but not nearly often enough to depend upon.
Just enough magic to mix things up a bit.
-- Edit to address more recent comments --
@2012rcampion, the answer to your question depends upon whether there is any magic nearby and under the subconcious control of the scientist at the moment when the feather and cannonball are released. If no magic is nearby, the experiment runs as it does in our world. If magic is nearby, it runs like the scientist wants it to. The difference isn't significant when the magical effect is big and obvious, or when the test runs to its expected conclusion. The problem arises when the test goes contrary to those expectations. Was it magic or was it that single abberant result which invalidates the well-established theory.
@Hurkyl, Science is served not only by its ability to imagine how things might work, but also by its mandate to discard any theory which fails even once. If magic is a possible explanation to any event, regardless of how rare and unlikely that involvement might be, Science looses its ability to enforce that mandate.