In the standard model of particle physics, there are three generations of quarks (up/down, strange/charm, and top/bottom), along with three generations of leptons (electron, muon, and tau). All of these particles have been observed experimentally, and we don't seem to have seen anything new along these lines. A priori, this doesn't eliminate the possibility of a fourth generation, but the physicists I've spoken to do not think additional generations are likely.
Question: What sort of theoretical or experimental reasons do we have for this limitation?
One reason I heard from my officemate is that we haven't seen new neutrinos. Neutrinos seem to be light enough that if another generation's neutrino is too heavy to be detected, then the corresponding quarks would be massive enough that new physics might interfere with their existence. This suggests the question: is there a general rule relating neutrino masses to quark masses, or would an exceptionally heavy neutrino just look bizarre but otherwise be okay with our current state of knowledge?
Another reason I've heard involves the Yukawa coupling between quarks and the Higgs field. Apparently, if quark masses get much beyond the top quark mass, the coupling gets strong enough that QCD fails to accurately describe the resulting theory. My wild guess is that this really means perturbative expansions in Feynman diagrams don't even pretend to converge, but that it may not necessarily eliminate alternative techniques like lattice QCD (about which I know nothing).
Additional reasons would be greatly appreciated, and any words or references (the more mathy the better) that would help to illuminate the previous paragraphs would be nice.
Answer
There are very good experimental limits on light neutrinos that have the same electroweak couplings as the neutrinos in the first 3 generations from the measured width of the $Z$ boson. Here light means $m_\nu < m_Z/2$. Note this does not involve direct detection of neutrinos, it is an indirect measurement based on the calculation of the $Z$ width given the number of light neutrinos. Here's the PDG citation:
http://pdg.lbl.gov/2010/listings/rpp2010-list-number-neutrino-types.pdf
There is also a cosmological bound on the number of neutrino generations coming from production of Helium during big-bang nucleosynthesis. This is discussed in "The Early Universe" by Kolb and Turner although I am sure there are now more up to date reviews. This bound is around 3 or 4.
There is no direct relationship between quark and neutrino masses, although you can derive possible relations by embedding the Standard Model in various GUTS such as those based on $SO(10)$ or $E_6$. The most straightforward explanation in such models of why neutrinos are light is called the see-saw mechanism
http://en.wikipedia.org/wiki/Seesaw_mechanism
and leads to neutrinos masses $m_\nu \sim m_q^2/M$ where $M$ is some large mass scale on the order of $10^{11} ~GeV$ associated with the vacuum expectation value of some Higgs field that plays a role in breaking the GUT symmetry down to $SU(3) \times SU(2) \times U(1)$. If the same mechanism is at play for additional generations one would expect the neutrinos to be lighter than $M_Z$ even if the quarks are quite heavy. Also, as you mentioned, if you try to make fourth or higher generations very heavy you have to increase the Yukawa coupling to the point that you are outside the range of perturbation theory. These are rough theoretical explanations and the full story is much more complicated but the combination of the excellent experimental limits, cosmological bounds and theoretical expectations makes most people skeptical of further generations. Sorry this wasn't mathier.
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