If there's one single experiment in history of science related to quarks, the first thing coming to my mind is the socalled "November revolution", where the charm quark was discovered, or more precisely put, charmonium has been found, the particle which we call ##J/\psi## since then. However, it was not discovered at CERN but in parallel at the same time in 1974 at the Stanford Linear Accelerator Center (SLAC) and at the Brookhaven National Laboratory (BNL). It was one of the triumphes of theory, having predicted the existence of a fourth quark flavor in order to explain the suppression of flavor-chaning neutral currents (Bjorken, Glashow 1964 and Glashow, Iliopoulus, Maiani 1970; nowadays known as the GIM mechanism and one of the cornerstones of the electroweak sector of the Standard Model, Quantum Flavor Dynamics).
Somwhat later, a 3rd generation of quarks has been predicted in order to explain CP violation (Kobayashi, Maskawa 1973). The bottom quark was discovered in 1977 at Fermilab, and the top quark, the hitherto last guy in the club, also at Fermilab in 1995.
CERN is most famous for the discovery of the gauge bosons of the weak interaction, the W- and Z0 bosons in 1983 and, of course, more recently the discovery of the Higgs boson (2012).