A number of beliefs traditionally regarded as metaphysical are challenged by modern physics.
Absolute Space and Time
Many traditional metaphysicians have argued for positions on the nature of space and time. Leibniz thought that space and time were relational rather than absolute (that is, that the only facts about space and time are facts about the spatial and temporal relations of particular objects), while Newton thought that space and time were absolute. (Kant argued for the compromise view that space and time are "empirically real, but transcendentally ideal" -- roughly, that Newton was right about the "empirical world" but not about things in themselves. One substantive difference implied by Newton's disagreement with Leibniz: for Leibniz, all facts about motion are relational, so we can say that object A is moving relative to object B (and vice versa), but there is no absolute fact about whether an object is in motion at a constant speed or at rest. If there were only a single object in the universe, there would be no fact about whether it was or was not moving at a constant speed.
On this issue, common sense surely agrees with Newton rather than Leibniz. However, in relativity theory it turns out that Leibniz was right about this particular point. There is no absolute fact about whether an object is in motion, only relative facts about which objects are in motion relative to which others.
Another related issue: if space and time were absolute, then distances and time intervals would be absolute. But they aren't: the distance in space between two objects, and the distance in time between two events, are relative to one's frame of reference.
(However, it is important to remember that it does not follow that there are no absolute facts. For Einstein, as for Newton, for instance, acceleration is not relative to a frame of reference. Similary, the separation of two events in spacetime remains the same even though separation in space and separation in time are relative.)
Kant thought he could prove a priori that every event has a sufficient cause, i.e. that determinism is true of the physical world. Quantum physics appears to establish that determinism is not only not a priori, but is not even true.
Even more disturbing than the loss of determinism is the loss of determinacy. QM appears to show that questions about the basic properties of fundamental particles (such as position, momentum, spin) do not have determinate values prior to observation. Bell's theorem together with experimental work appears to rule out the possibility that the problem is only epistemological -- that these properties have determinate values and the only problem is that they are not accessible to observation.
"Everything is Relative"
Relativity theory is sometimes associated rather thoughtlessly with the slogan that "everything is relative." However, this is a completely inaccurate and misleading assertion. On the contrary, relativity theory is an attempt to achieve a more objective picture of the universe by discovering which features are absolute, and explaining exactly what the relative features are relative to and why.
Idealism (The World as Mind-Dependent)
QM is sometimes regarded as vindicating something very like Berkeleian idealism, as showing that the properties of the physical world depend on facts about observers. But notice two things. (1) In QM, unlike in Berkeleian idealism, it is not the case that everything is observer-dependent. The exact position of a particle depends on (is somehow produced by) its measurement, but its location regarded as a probability distribution is entirely objective. (2) Moreover, dependence on measurement is not necessarily the same thing as dependence on the mind. There seems to be disagreement among physicists about whether consciousness plays any essential role in measurement. The idea that fundamental properties are mind-dependent as well as measurement-dependent seems to be a minority view.