The Latest Results
To date, no such particles have been discovered experimentally: "No significant deviations from standard model predictions have been observed.", in the ongoing search of supersymmetry at the Large Hadron Collider (LHC) according to a combined report of the ATLAS and CMS experiments released in pre-print form today.
In admittedly mildly model dependent searches, "neutralinos" (which are fermions that are electrically neutral superpartners of the electroweak gauge bosons of the Standard Model) are ruled out for masses of up to about 350 GeV (about twice the top quark mass) and "charginos" (which are fermions that are electrically charged superpartners of the charged electroweak gauaged bosons including non-Standard Model charged Higgs bosons) are ruled out for masses up to about 750 GeV (more than four times the top quark mass).
This does not disprove the existence of SUSY in and of itself, but it does narrow the parameter space to SUSY to one that is indistinguishable from the Standard Model, at energies up to first run LHC energies (i.e. proton-proton collisions at sqrt(s)=8 TeV with an integrated luminosity of about 20 fb-1), when taken together with other evidence.
Other Searches For Sparticles And SUSY Higgs Bosons.
Searches for other sparticles have generally ruled these particles out for masses less than hundreds of GeVs to several TeV.
SUSY theories also predict a minimum of five Higgs bosons (a light and heavy scalar neutral Higgs boson, a pseudoscalar neutral Higgs boson, and a positively and negatively charged Higgs boson). No non-Standard Model Higgs bosons have been observed, although the exclusions are only up to the hundreds of GeV and the data can't yet definitively rule out a scenario in which two or three SUSY Higgs bosons that collectively behave like the Standard Model Higgs bosn are nearly degenerate in mass around 125 GeV-126 GeV.
SUSY Bounds From The Anomalous Magnetic Moment of the Muon
The anomalous magnetic moment of the muon in indirectly effected by the masses of all existing gauge bosons that interact via electromagnetism. The current value of this physical constant implies that any undiscovered bosons with electroweak interactions (which would include any SUSY boson) must have certain minimum masses (citing this source) and the lower bounds are even greater if the discrepancy between the current experimental value and the theoretical value are actually fully consistent with each other. These are as follows:
In summary we found the following particles capable of explaining the current discrepancy, assuming unit couplings: 2 TeV (0.3 TeV) neutral scalar with pure scalar (chiral) couplings, 4 TeV doubly charged scalar with pure pseudoscalar coupling[.]. . .The W and Z bosons and gluons are vector bosons with chiral couplings. I don't know if the couplings of the Standard Model Higgs boson or its additional supersymmetric counterparts do or do not have chiral couplings.
We also derive the following 1σ lower bounds on new particle masses assuming unit couplings and that the experimental anomaly has been otherwise resolved: a doubly charged pseudoscalar must be heavier than 7~TeV, a neutral scalar than 3 TeV[.]
The supersymmetric counterparts of the Standard Model quarks and charged leptons are charged scalar bosons (singly charged in the case of the selectron smuon and stau, and fractionally charged in the case of the squarks).
The superpartners of the neutrinos are neutral scalar bosons (the selectron sneutrino, the smuon sneutrino and the stau sneutrino, not to be confused with neutralinos which are not superpartners of the neutrinos). One can imagine a slight SUSY variant in which some or all of these bosonic superpartners have J=0 but have pseudoscalar rather than scalar parity. Of the supersymmetric additional Higgs bosons, at least one would be a neutral scalar, one would be a neutral pseudoscalar, and two would be singly charged scalars.
These bosons must have at least 300 GeV of mass if they have chiral couplings, at least 2 TeV of mass if they don't have chiral couplings, and at least 3 TeV of mass if the anomalous magnetic moment of the muon actually has its theoretical value but there is experimental error in the ultraprecision measurement of it.
Non-minimal SUSY theories often have even more Higgs bosons, some of which are doubly charged, which the anomalous magnetic moment of the muon requires be at least 4 TeV if it is pseudoscalar and 7 TeV if the anomalous magnetic moment is due to experimental error rather than being a true discrepancy between theory and reality.
The Impact of B and L Number Violations On SUSY Parameter Space
Furthermore, most SUSY theories do not separately conserve baryon number (B) or lepton number (L), but only B-L, a property that leads to phenomena such as neutrinoless beta decay and flavor changing neutral current interactions. Critically, the rates of these phenomena are generically functions of sparticle masses and increase as sparticle masses increase. So, if a SUSY theory is fairly minimal and typical in all other respects, and has sparticles too heavy to otherwise be detected even inconclusively at current LHC energies, neutrinoless beta decay rates should be high and flavor changing neutral currents should occur relatively frequently.
No such interactions have been observed and strict constraints on the maximum rates at which these kinds of interactions can occur have been established experimentally. Current neutrinoless beta decay searches (even one in Moscow which claims to have seen a signal not seen by any other experiments) are sufficient strict that they effectively rule out sparticles with masses in excess of those that have been ruled out by the LHC.
Now, obviously, a theorist can go back to the drawing board and come up with a SUSY-type theory that suppresses or rules out B number and L number non-conservation interactions to some arbitrary scale beyond the scope of current experiments. But, experimental data now rule out pretty much every SUSY variation that isn't modified in this way.
Searching For Particular SUSY Particles v. Searching For Any SUSY Particle
Also, keep in mind that these are generally two sigma exclusions, covering a range where it is 95% certain that there are no sparticles of the type sought. A one sigma exclusion (which would be a range over which there is a 68% probability that there is no sparticle of less than the applicable mass cutoff) would be higher. Now if you want any confidence that a particular particle isn't in a particular mass range, a two or three sigma cutoff is appropriate.
But, suppose that the question you really want to ask is "are there any superpartners of less than a given mass?" If, for model dependent reasons, the lightest supersymmetric particle (LSP) should have several companion supersymmetric particles of order of magnitude similar mass, then the one sigma cutoff in each of the individual cutoffs ought to be relevant, because a search for each of the lighter SUSY particles ought to reveal at least one of the lighter SUSY particles with that significance.
If there are a dozen or so undiscovered supersymmetric particles out there and several of them are relatively light, the odds that we would receive a strong hint of at least one of them in some kind of data, even if we didn't get any experimental hint of others and got only a sub-discovery level indication of another, are still much greater than the odds that we would actually discover even a single SUSY particle.
Thus, the breadth of the null result for beyond the Standard Model physics also disfavors SUSY scenarios with a whole suite of sparticles with masses "just over the horizon" of current experimental limits. If the full suite of particles predicted by SUSY theories existed we would expect to see a variety of low to moderate significance anomalies and indirect effects at lower energies that are not observed, even in the absence of any definitive discovery of a particular sparticle at or near the threshold for discovery in high energy physics.
The Impact Of The Higgs Boson Discovery and Conclusion
The null results of these searches, the discovery of the 125.9 GeV Higgs boson that is identical in all measured respects to date to the Standard Model Higgs boson, and various non-collider data, taken as a whole largely rule out "minimal" variations of SUSY at the electroweak energy scale where sparticles had been expected when the theory was originally proposed, fully "natural" version of SUSY, and a wide variety of other variations and parameter spaces for supersymmetric theories.
A Higgs boson at the mass observed also resolves what could have been a critical flaw in the Standard Model. In scenarios with many other possible Higgs boson masses, or with no Higgs boson at all, the equations of the Standard Model broke down at energies well under the "GUT scale". But, as it is, the Standard Model is "ultraviolet complete" (i.e. its equations produce results that make sense even at high energies).
Thus, SUSY is not necessary to have a mathematically coherent Standard Model at high energies. The Standard Model may be a bit ugly, but it produces coherent predictions, even at extremely high energies that could never be replicated experimentally or through astronomy observations (which can't directly observe the earliest moments of the universe when energy scales were that high).
It is currently fashionable to propose SUSY models in which all but a few supersymmetric particles have mases of several TeV to tens of TeV.