Are the properties assigned to quarks meaningful? Suspect this may have been asked before, but can't find it. My question is: If you can never have a free quark, what sense does it make to attribute properties to them, since you can never experimentally isolate a quark to measure that property (for example its mass)?
 A: Here are the quarks as posited in the standard model:


*The masses should not be taken too seriously, because the confinement of quarks implies that we cannot isolate them to measure their masses in a direct way. The masses must be implied indirectly from scattering experiments. The numbers in the table are very different from numbers previously quoted and are based on the July 2010 summary in Journal of Physics G, Review of Particle Physics, Particle Data Group. A summary can be found on the LBL site. These masses represent a strong departure from earlier approaches which treated the masses for the U and D as about 1/3 the mass of a proton, since in the quark model the proton has three quarks. The masses quoted are model dependent, and the mass of the bottom quark is quoted for two different models. But in other combinations they contribute different masses. In the pion, an up and an anti-down quark yield a particle of only 139.6 MeV of mass energy, while in the rho vector meson the same combination of quarks has a mass of 770 MeV! The masses of C and S are from Serway, and the T and B masses are from descriptions of the experiments in which they were discovered. 

These on the table are also called the current quark masses, and are the masses entered in the Lagrangian which leads to the calculation of the crossections. The masses dividing the nucleon or resonance mass by the number of quarks are called constituent masses, which arise from the relativistic kinematics of the sea of quarks, antiquarks and gluons within a hadron.
You state:

If you can never have a free quark, what sense does it make to attribute properties to them, since you can never experimentally isolate a quark to measure that property (for example its mass)?

As the quote says, the sense comes from fitting scattering crossections and decays of resonances with a mathematical model, with great accuracy: the standard model of particle physics.. The model not only fits the existing data, but also predicts new phenomena. The properties are measured by the fits to the data, and by the use of conservation laws.
A: Confinement implies that there is no unique definition of the quark mass. In particular, there is no analog of the pole mass that can be used to define the mass of the electron. However, the mass is a parameter in the lagrangian, and in any regularization scheme (MSbar, lattice, etc) the quark masses are rigorously defined. Also, the relation between the quark masses in different regularization schemes can be computed in perturbation theory, so that there is a well defined strategy for comparing the masses determined using different definitions. 
The masses of the quarks determine the masses of hadrons (the hadron masses are finite in the limit $m_q\to 0$, but this does not change the fact that their precise values depend om $m_q$), and can therefore be extracted from experiment. These are the values that you find quoted in the Particle Data Tables and on wikipidia.  
