I strongly suspect that the Standard Model of Particle Physics is complete (except for gravity), by which I mean that it describes all fundamental particles (i.e. non-composite particles) other than possibly a massless spin-2 graviton, and all forces (other than gravity), and that the equations of the three Standard Model forces are basically sound.
I likewise strongly suspect that the running of the experimentally measured constants of the Standard Model with energy scale, according to their Standard Model beta functions, is basically correct, although these beta functions may require slight modification (that could add up to something significant at very high energies) to account for gravity.
This said, I do not rule out the possibility that some deeper theory explains everything in the Standard Model more parsimoniously, or that there are additional laws of nature that while not contradicting the Standard Model, further constrain it. Also, I recognize that neutrino mass is not yet well understood (but strongly suspect that neither a see-saw mechanism, nor Majorana neutrinos, are the correct explanation).
There are some global tests of the Standard Model and other kinds of reasoning that suggest this result. Twenty-two such reasons are set forth below.
Reasoning Up To Future Collider Energy Scales
1. Experimentally measured W and Z boson decay branching fractions are a tight match to Standard Model theoretically prediction. This rules out the existence of particles that interact via the weak force with a mass of less than half of the Z boson mass (i.e. of less than 45.59 GeV).
2. The consistency of the CKM matrix entries measured experimentally with a three generation model likewise supports the completeness of the set of six quarks in the Standard Model. If there were four or more generations, the probabilities of quark type transitions from any given quark wouldn't add up to 100%.
3. The branching fractions of decaying Higgs bosons are a close enough match to the Standard Model theoretical prediction that new particles that derive their mass from the Higgs boson with a mass more than about 1 GeV and less than about half of the Higgs boson mass (i.e. about 62.6 GeV) would dramatically alter these branching fractions. The close match of the observed and Standard Model Higgs boson also disfavors the composite Higgs bosons of technicolor theories.
4. The muon g-2 measurement is consistent with the BLM calculation of the Standard Model expectation for muon g-2 and I strongly suspect that the BLM calculation is more sound than the other leading calculation of that value. If the BLM calculation is sound, then that means that nothing that makes a loop contribution to muon g-2 (which is again a global measurement of the Standard Model) that does not perfectly cancel out in the muon g-2 calculation has been omitted. The value of muon g-2 is most sensitive to new low mass particles, with the loop effects of high mass particles becoming so small that they effective decouple from the muon g-2 calculation. But this does disfavor new low mass particles in a manner that makes the exclusion from W and Z boson decays more robust.
5. The Standard Model mathematically requires each generation of fermions to contain an up-type quark (excluded below 1350 GeV), a down-type quark (excluded below 1530 GeV), a charged lepton (excluded below 100.8 GeV), and a neutrino. Searches have put lower bounds on the masses of new up-type quarks, down-type quarks, and charged leptons, but the most powerful constraint is that there can't be a new active neutrino with a mass of less than 45.59 GeV based upon Z boson decays. Yet, there is observational evidence constraining the sum of all three of the neutrino mass eigenstates to be less than about 0.1 eV and there is no plausible reason for there to be an immense gap in neutrino masses between the first three and a fourth generation neutrino mass. There are also direct experimental search exclusions for particles predicted by supersymmetry theories and other simple Standard Model extensions such as new heavy neutral Higgs bosons (with either even or odd parity) below 1496 GeV, exclusions for new charged Higgs bosons below 1103 GeV, W' bosons below 6000 GeV, Z' bosons below 5100 GeV, stable supersymmetric particles below 46 GeV, unstable supersymmetric neutralinos below 380 GeV, unstable supersymmetric charginos below 94 GeV, R-parity conserving sleptinos below 82 GeV, supersymmetric squarks below 1190 GeV, and supersymmetric gluinos below 2000 GeV. There are also strong experimental exclusions of simple composite quark and composite lepton models (generally below 2.3 TeV for some cases and up to 24 TeV in others) and similar scale experimental exclusions of evidence for extra dimensions that are relevant to collider physics.
6. In the Standard Model, fermions decay into lighter fermions exclusively via W boson interactions, and the mean lifetime of a particle in the Standard Model is something that can be calculated. So, it ought to be impossible for any fermion to decay faster than the W boson does. But, the top quark decays just 60% slower than the W boson, and any particle that can decay via W boson interactions that is more massive than mass range for new Standard Model type fermions that has not been experimentally excluded should have a mean lifetime shorter than the W boson.
7. Overall, the available data on neutrino oscillations, taken as a whole, disfavors the existence of a "sterile neutrino" that oscillates with the three active Standard Model neutrinos.
8. It is possible to describe neutrino oscillation as a W boson mediated process without resort to a new boson to govern neutrino oscillation.
9. There are good explanations for the lack of CP violation in the strong force that do not require the introduction of an axion or another new particle. One of the heuristically more pleasing of these explanations is that gluons are massless and hence do not experience the passage of time and hence should not be time asymmetric (which CP violation implies).
10. Collider experiments, moreover, have experimentally tested the Standard Model at energies up to those present a mere fraction of a second after the Big Bang (by conventional cosmology chronologies). Other than evidence for lepton universality violations, there are no observations which new particles or forces are clearly necessary to explain at colliders with new physics.
11. I predict that lepton universality violations observed in semi-leptonic B meson decays, but nowhere else, will turn out to be due to a systemic error, most likely, in my view, a failure of energy scale cutoffs that were designed to exclude electrons produced in pion decays to be excluded as expected. To a great extent, in addition to a general Standard Model correctness Bayesian prior, this is also due to the fact that semi-leptonic B meson decays in the Standard Model are a W boson mediated process indistinguishable from many other W boson mediated processes in which lepton universality is preserved.
12. The consistency of the LP&C relationship (i.e. that the sum of the square of the masses of the fundamental particles of the Standard Model is equal to the square of the Higgs vacuum expectation value) with experimental data to the limits of experimental accuracy (with most of the uncertainty arising from uncertainty in the measurements of the top quark mass and the Higgs boson mass), suggests that this is a previously unarticulated rule of electroweak physics and that there are no fairly massive (e.g. GeV scale) fundamental fermions or bosons omitted from the Standard Model. Uncertainties in the top quark mass and Higgs boson mass, however, are sufficient large that this does not rule out very light new fundamental particles (which can be disfavored by other means noted above, however). The LP & C relationship, if true, also makes the "hierarchy problem" and the "naturalness" problem of the Standard Model, that supersymmetry was devised to address, non-existent.
13. I suspect that the current Standard Model explanation for quark, charged lepton, W boson, Z boson and Higgs boson masses, which is based upon a coupling to the Higgs boson understates the rule played by the W boson in establishing fundamental particle masses underscored by the fact that all massive fundamental particles have weak force interactions and all massless fundamental particles do not have weak force interactions, and by cryptic correlations between the CKM and PMNS matrixes which are properties of W boson mediated events, and the fundamental particle masses. A W boson centric view of fundamental particle mass is attractive, in part, because it overcomes theoretical issues associated with Standard Model neutrinos having Dirac mass in a Higgs boson centric view.
Astronomy and Cosmology Motivated Reasons
14. The success of Big Bang nucleosynthesis supports that idea that no new physics is required, and that many forms of new physics are ruled out, up to energy scales conventionally placed at ten seconds after the Big Bang and beyond.
15. The Standard Model is mathematically sound and at least metastable at energy scales up to the GUT scale without modification. So, new physics are not required at high energies. Consideration of gravity when determining the running of the Standard Model physical constants to high energies may even take the Standard Model from merely being metastable to being just barely stable at the GUT scale. The time that would elapse from the Big Bang t=0 to GUT or Planck energies at which the Standard Model may be at least metastable is brief indeed and approaches the unknowable. Apart from this exceeding small fraction of a second, energies above this level don't exist in the universe and new physics above this scale essentially at the very moment of the Big Bang could explain its existence.
16. Outside the collider context, dark matter phenomena, dark energy phenomena, cosmological inflation, and matter-antimatter asymmetry, are the only observations that might require new physics to explain.
17. A beyond the Standard Model particle to constitute dark matter is not necessary because dark matter can be explained, and is better explained, as a gravitational effect not considered in General Relativity as applied in the Newtonian limit in astronomy and cosmology settings. There are several gravitational approaches that can explain dark matter phenomena.
18. There are deep, general, and generic problems involved in trying to reconcile observations to collisionless dark matter particle explanations, some of which are shared by more complex dark matter particle theories like self-interacting dark matter, and as one makes the dark matter particle approach more complex, Occam's Razor disfavors it relative to gravitational approaches.
19. Direct dark matter detection experiments have ruled out dark matter particles even with cross-sections of interaction with ordinary matter much weaker than the cross-section of interaction with a neutrino for masses from somewhat less than 1 GeV to 1000 GeV, and other evidence from galaxy dynamics strongly disfavors truly collisionless dark matter that interacts only via gravity. This limitation, together with collider exclusions, in particular, basically rule out supersymmetric dark matter candidates which are no longer theoretically well motivated.
20. Consideration of the self-interaction of gravitational fields in classical General Relativity itself (without a cosmological constant), can explain the phenomena attributed to dark matter and dark energy without resort to new particles, new fields, or new forces, and without the necessity of violating the conservation of mass-energy as a cosmological constant or dark energy do. The soundness of this analysis is supported by analogy to mathematically similar phenomena in QCD that are well tested. Explaining dark energy phenomena with the self-interaction of gravitational fields removing the need for a cosmological constant also makes developing a quantum theory of gravity fully consistent in the classical limit with General Relativity and consistent with the Standard Model much easier. There are also other gravity based approaches to explain dark energy (and indeed the LambdaCDM Standard Model of Cosmology uses the gravity based approach of General Relativity with a cosmological constant to explain dark energy phenomena).
21. The evidence for cosmological inflation is weak even in the current paradigm, and it is entirely possible and plausible that a gravitational solution to the phenomena attributed to dark matter and dark energy arising from the self-interaction of gravitational fields, when fully studied and applied to the phenomena considered to be evidence of cosmological inflation will show that cosmological inflation is not necessary to explain those phenomena.
22. There are plausible explanations of the matter-antimatter imbalance in baryons and charged leptons that is observed in the universe that do not require new post-Big Bang physics. In my view, the most plausible of these is the possibility that there exists an antimatter dominated mirror universe of ours "before" the Big Bang temporally in which time runs in the opposite direction, consistent with the notion of antimatter as matter moving backward in time and with time flowing from low entropy to high entropy. So, no process exhibiting extreme CP asymmetry (and baryon and lepton number violation) and limited to ultra-high energies present in the narrow fraction of a second after the Big Bang that has not been explored experimentally is necessary.