An aspect of the discovery of the Higgs boson to celebrate is the possibility of prediction in science — in this case, the prediction that a certain particle should exist so that the world can behave as it does, and even a prediction of its approximate mass, which made it possible to design an accelerator (the Large Hadron Collider) that could accelerate protons to a high enough energy to be able, in collisions with nuclei, to produce the predicted particle if it has the predicted mass. The accelerator was built, the experimentalists looked, and they found something at the right mass. They will study the reactions that particle has, and the ways it decays (falls apart into other particles), to try to pin down whether it in fact has the right properties besides the right mass to be the Higgs boson.
There are some other examples of predicting and finding previously unsuspected particles.
In the 1860s, building on preliminary, partial work by others, Mendeleev was able to bring order to all the known elements in his famous periodic table. Moreover, he correctly interpreted holes in his table as representing elements that had yet to be discovered. For example, he not only predicted the existence of germanium but also predicted its approximate atomic weight and chemical properties, and he was right. In all, he correctly predicted 8 elements that were unknown at the time. The Wikipedia article shows his debt to the ancient Sanskrit grammarian Panini, who had recognized similar kinds of order among the sounds of human speech.
At the time, no one, including Mendeleev, had any way to explain the ordering of the elements made manifest in the periodic table. It was 40 years later that Rutherford and his coworkers discovered that atoms consist of a tiny, extremely dense positively-charged core (the “nucleus”) surrounded by negatively charged electrons (which had recently been discovered by Thompson). A few years later experiments showed that the order of elements in the periodic table simply reflects the number of electrons in the atom (1 for hydrogen, 2 for helium, etc.).
In 1928 Dirac created the famous “Dirac equation”, constituting a version of quantum mechanics that is consistent with special relativity (the earlier Schrodinger equation is not consistent with relativity, though it remains useful in the nonrelativistic limit). An odd feature of the Dirac equation was its prediction of electron-like particles with negative energy, which led Dirac with some reluctance to predict the discovery of an “anti-electron”, an electron-like object with positive charge. The positron was soon found by Carl Anderson at Caltech, with the predicted properties.
In the 1920s there was a puzzle in “beta decay”, in which a nucleus emits an electron (and metamorphoses into a nucleus with one additional positive charge; see my post on neutron decay). The puzzle was that the energies of the parent and daughter nuclei were known (from their masses) to be fixed quantities, but the electron was observed to have a broad range of energies, not simply the difference of the two nuclear energies. This was an apparent violation of the well established principle of energy conservation. There were suggestions that perhaps energy is not conserved in nuclear interactions, but Pauli could not accept that. In 1930 he proposed that the electron is not the only particle emitted in beta decay, that there is also another particle emitted but not observed. This implied that the unseen particle must have no electric charge, as otherwise it would be easily detected, and in fact it must also not interact with nuclei through the “strong interaction”, because again this would make the neutrino easily detectable. Also, the maximum observed energy of the electron was experimentally found to be about equal to the energy difference of the parent and daughter nuclei, which implied that the unseen particle must have very little mass. Pauli had predicted what is now called the neutrino, with specific properties: no electric charge, very small mass, no strong interactions.
The neutrino was observed directly only much later, in 1956, when Reines and Cowan placed detectors behind thick shielding next to a nuclear reactor at the Savannah River Plant in South Carolina. Neutrino reactions are very rare, but the flux of neutrinos was so large that occasionally the experimenters observed “weak” interactions of the neutrinos with matter. The properties of the neutrino matched Pauli’s predictions.
In the early 1960s Gell-Mann and Ne’eman independently were able to classify the large zoo of “elementary” particles into groups of octets and decuplets. There was a decuplet (of 10 particles) arranged in a triangle, like bowling pins, in which the particle at the point was unknown. Gell-Mann was able not only to predict the existence of this particle, which he called the Omega-minus, but he also predicted its charge and mass. A hunt for the Omega-minus was successful, and it had the predicted properties.
As was the case with Mendeleev’s periodic table, at first there was no explanation for the “why” of octet and decuplet groupings of the known particles. Soon however Gell-Mann and Zweig independently proposed that each “baryon” (heavy) particle was made of 3 “quarks” with unusual fractional electric charges, and each “meson” was made of a quark and antiquark. At first somewhat controversial, intense experimental work and closely related theoretical work by Feynman made it clear that the quark model does indeed explain the “periodic table of the particles”.
The creation of antiprotons occurred in a context very similar to the creation of the Higgs boson. The Berkeley Bevatron was a particle accelerator built in 1954, designed to accelerate protons to an energy sufficient to produce antiprotons if, as everyone predicted, the antiproton would have the same mass as a proton (but negative charge). This design criterion was similar to the design consideration for the Large Hadron Collider, that of acclerating protons to an energy large enough to create Higgs bosons. Because by 1954 many particles were known to have antiparticle partners, it was not a surprise when antiprotons were indeed produced by the Bevatron.
I’ve listed some major predictions that were successful. However, it seems to me that “postdiction” is more common. For example, no one predicted that the rings of Saturn can be braided. When spacecraft first returned closeups of the rings, scientists were startled to see braided rings. A lot of work went into understanding these unusual structures (the key turned out to be the role of small “shepherd” moons).