How can Lorentz contraction be "directly" measured? If one is watching a relativistic object of e.g. spherical shape, which emits enough light to be detectable, it will, despite being Lorentz contracted, appear of its natural shape, although rotated. This phenomenon is called Terrel rotation$^\dagger$.
Citing wikipedia on Lorentz contraction, "length contraction is the phenomenon of a decrease in length measured by the observer of an object which is traveling at any non-zero velocity relative to the observer". So, how can the observer actually measure this decrease in length? Can it be somehow done in a non-relativistic regime of a measurement apparatus?
$^\dagger$Russian version of the page gives more detail with some pictures
 A: The problem with experimental measurement of Lorentz contraction is that the only objects we've managed to accelerate to near light speeds are elementary particles, and they're pointlike so they can't contract.
Well, not quite. The RHIC accelerator collides heavy nuclei, and they do have a non-zero radius. The trouble is that it's hard to measure the size of a nucleus. However what you can do is calculate the dynamics of the collision, and if you do that you find it matches the results expected if the nuclei are Lorentz contracted into disks. I would certainly regard this as experimental confirmation of Lorentz contraction, but since it's an indirect measurement I guess it does leave the door open for the sceptics.
A: This depends quite a bit on what you're willing to accept as "direct."
The magnetic force between two parallel current-carrying wires can be interpreted as being due to Lorentz contraction, and that's quite easy to measure -- you can do it with a battery and some strips of aluminum foil.
Some measurements can be interpreted as showing time dilation, but in a different frame they show length contraction. For example, in the earth's frame of reference, we explain the anomalously high flux of cosmic-ray muons at the earth's surface as being due to time dilation: their half-lives are lengthened because of their motion. But in the frame of the muons, their survival is due to the length contraction of the earth's atmosphere.
