Non-stock dinosaurs are really numerous, so it could be useful knowing the scientific history at least of the most prominent ones. Of course we shouldn't omit their more popular fellows, so you'll find also references to T. rex, Triceratops, and even some non-dinosaurs like Pteranodon in the folder below.
EARLY AND MIDDLE 1800: the first discoveries In 1801, in full Napoleonic age, Baron Georges Cuvier described the first "antediluvian reptile": the "Ptero-dactylo" — later re-named Pterodactylus by other scientists which chose to follow the Linnean convention to name animals with latin italicized names. Few years later the founder of Paleontology named the first marine reptile: the "mosasaur" (Mosasaurus), whose jaws were re-discovered in the Netherlands. These two creatures showed that before the "mammal era" populated by mammoths mastodons megatheres (already known since the late 1700) there was an era dominated by reptiles, named the "reptile era" indeed (what today is called the Mesozoic). But there weren't still dinosaurs. The first dinosaurs came to light about twenty years after the "ptero-dactylo".
LATE 1800: the "Bone Wars" After the first American discoveries above, two palaeontologists of the North-East of the USA, Edward D. Cope & Othniel C. Marsh, were attracted by the great plenty of fossil material casually found in the Far West. Their wish of glory and scientific prestige caused them becoming archrivals for their whole life. They obsessively searched for the most spectacular dinosaur possible and then published the discover in scientific papers — both arrived to the point to destroy some fossils found by the other scientist! However, we have to thank them if so many dinosaurs were found in this period: among them, just the most famous dinosaurs in the XX century. (Interest in dinosaurs was still bland at Marsh's & Cope's times). Many names of dino-groupings were also created within the "wars": Theropods, Sauropods, Ornithopods, Stegosaurians, Ceratopsians. Some of these groups were invented just to include bone-wars dinosaurs. One of the first animals described by Marsh was the today-obscure sauropod Atlantosaurus immanis (immanis = immense), publicized as "the biggest creature that ever lived" (extimated even 40 m/130 ft long, twice a Real Life apatosaurus and even longer than a Real Life diplodocus!). Cope responded with his Camarasaurus supremus (supremus = the biggest), also initially extimated up to 40 m/130 ft of length. But it was Marsh that won the sauropod-competition describing the two most famous sauropods, Apatosaurus and Diplodocus indeed (but also Barosaurus). It was also Marsh the responsible of both the notorious "Brontosaurus" misunderstanding, and the classic theory about water-living sauropods lasted until the late 1900. It's worth noting that both scientists often discovered the same animals, but gave them different names; usually the names coined by Marsh are still valid today, while the Cope's ones are simple invalid synonyms; exceptions are Camarasaurus, Coelophysis & Monoclonius, all Cope's creations. But the Marsh ones include names like Stegosaurus, Triceratops, Allosaurus other than Apatosaurus, Brontosaurus, Diplodocus. Also named by Marsh were: the horned carnivore Ceratosaurus, the ornithopods Camptosaurus and Dryosaurus, the small carnivore Coelurus, the ceratopsid Torosaurus, the ankylosaur Nodosaurus, and Ornithomimus, the first bird-like dinosaur recognized as "bird-like". Curiously, Cope described some "sensational" animals that are not much known today: the huge allosaur Epanterias and the mysterious giant vertebra of Amphicoelias (which has recently become popular thanks to Internet). And it was Cope that discovered the first complete hadrosaur skeletons, named Trachodon copei (now called Anatosaurus copei, Edmontosaurus copei or Anatotitan copei, see Stock Dinosaurs) It's also worth of note the fact that some non-dinosaurs that are stock today were also found during the "bone-wars" (usually by Marsh): the pterosaur Pteranodon, the plesiosaur Elasmosaurus, the mosasaur Tylosaurus, and the mammal-like Dimetrodon. Not to mention some extinct big mammals, like Uintatherium & Brontotherium. More precisely, however, Elasmosaurus was discovered and described by Cope slightly before the beginning of the scientific competition: there is a curious story tied with the elasmo's reconstruction made by Cope (see "Heads or Tails?")
EARLY 1900: dinosaurs everywhere In this time the dino-groups that are the most familiar today (giant quadrupedal sauropods ceratopsians & stegosaurs and ERECT giant carnivores) made their triumphant entry in the western pop-culture. The old four-legged dragons of the british "crystal palace park" were replaced by much more diversified animals with long necks, horned heads, armored backs, upright stances, bird-like bills and so on. For the joy of pop-culture-makers this available diversity increased even more just in this period: in Europe, Asia, Africa, and expecially North-America were (sometimes re-) discovered many new kinds of dinosaurs that soon later joined their relatives in museums, paleo-art, and sometimes films and cartoons. Above all, they added more material for scientists to rebuild the mosaic of the dino-evolution. Among them, Harry G. Seeley was able to separate dinosaurs in two great branches: Saurischians & Ornithischians.
MIDDLE 1900 The middle portion of the XX century is sometimes known as "the dinosaur Middle Ages": from the 1930s to the 1970s few new dinosaur kinds were added to the list, and very few new theories about their life were ideated. The classic image of "big stupid beasts condemned to extinction" was dominant, filling many movies and popular reconstructions of the time. North America assisted the last findings of the former dino-rush — from Wyoming came Pachycephalosaurus, aka the modern prototype of the thick-headed dinosaurs. Then, in the sixties, it was discovered the huge graveyard of Coelophysis in New Mexico, making the coelophysis joining Plateosaurus as the most best-known early dinosaur (and leading the hypothesis that Coelophysis was cannibalistic). In Europe, "Megalosaurus" was still treated as a Wastebasket; however, the theropod Eustreptospondylus was deemed distinct from Megalosaurus in the 1930s. Also interesting were the dino-news from the asian Far East: the second dino-hunt in Mongolia (this time led by Russian scientists) revealed in the 1950s the eastern T.rex relative Tarbosaurus, the asian species of Saurolophus, and the huge claw of Therizinosaurus (other than several new specimens of Protoceratops, nicknamed the "sheep of the Cretaceous" just for its abundance). Meanwhile, in China, Young Chung Chien (the father of Chinese paleontology) announced the first well-preserved dinosaurs found in his country: the huge-necked sauropod Mamenchisaurus, the unicorn-like hadrosaur Tsintaosaurus, other than the first asian stegosaurs and carnosaurs, and the early Lufengosaurus — which started the tradition of portraying dinosaurs in postage-stamps.
THE 1970s AND 1980s: the Great Renaissance The dino-discover that dominated the 1970s was undoubtly Deinonychus, the "sickle-clawed dinosaur", described in Montana by John Ostrom as a cunning vicious hunter of big game (namely the ornithopod Tenontosaurus), so debunking the traditional vision of all dinosaurs as slow and foolish, and leading to the famous "Dinosaur Renaissance" led mainly by Ostrom's pupil Bob Bakker. Meanwhile, in Mongolia, the third historical expedition there (this time led by Polish scientists) note uncovered the famous combat between Velociraptor & Protoceratops. So a Canadian palaeontologist, Dale Russell, decided to put Deinonychus & Velociraptor in the same family, Dromaeosaurids. Also another Jurassic Park guy, Gallimimus, was found in Mongolia in the Seventies, as well as his huge relative Deinocheirus (better, the latter's forelimbs), and a variety of other animals (the flat-headed pachycephalosaur Homalocephale, the Mix-and-Match Critter Segnosaurus, the late-surviving sauropod Opisthocoelicaudia, and a whole herd of juvenile Pinacosaurus among the others). Souther, in China, Dong Zhiming started adding new dinosaurs to his predecessor Young's list: among them the stegosaur Tuojiangosaurus, the carnosaur Yangchuanosaurus, the club-tailed sauropod Shunosaurus, and also the huge-named Micropachycephalosaurus. Even souther, in India, a very fragmentary plesiosaur (Dravidosaurus) was wrongly publicized as "the last-surviving stegosaur". In South Africa, the curious tusked Heterodontosaurus and the more generic Lesothosaurus gave new light to the ornithischians' first evolutionary steps, as well as new more complete remains of Massospondylus did with the sauropodomorph branch. In Northern Africa a sail-backed animal, the duck-billed Ouranosaurus, joined the other more famous sailback, Spinosaurus. In Argentina Jose Bonaparte discovered the first armored sauropod, Saltasaurus, and the horned theropod Carnotaurus (which revealed the best print of skin ever in a large dinosaur), as well as several primitive dinosaurs (Riojasaurus, Mussaurus etc.) But the most primitive of them all, Staurikosaurus & Herrerasaurus, were not described by Bonaparte — Staurikosaurus was not even found in Argentina but in Brazil. The description of these two middle triassic small carnivores broke up for some time the dichotomy Saurischians vs Ornithischians, as they were believed too primitive to belong to either; today they are believed very unspecialized saurischians. In the USA, other than Deinonychus was announced the early jurassic Dilophosaurus (formerly believed a species of the "wastebasket taxon" Megalosaurus), as well as its possible prey, the small armored Scutellosaurus, the equally-armored but much larger ankylosaur Sauropelta, and still other new genera. Meanwhile (also in USA) James Jensen resurrected the old tradition of ballyhooing incredibly huge sauropods to the media: his Supersaurus was briefly "the biggest dinosaur ever" until the even bigger "Ultrasaurus" was announced by Jensen some years later. In Canada, Phil Currie found a huge herd of Centrosaurus dead together in a flood, and described Troodon as "the biggest-brained dinosaur". His colleague Dale Russell got this Up to Eleven thinking it could have become similar to a humanoid if survived to the extinction. Dale Russell also lumped Gorgosaurus into Albertosaurus (but judged Daspletosaurus distinct from the latter) and separated "Dromiceiomimus" from Ornithomimus. But the most prominent palaeontologist was perhaps Jack Horner. In the 1980s, his discover of the nests of the hadrosaur Maiasaura got ultimately the proof that some dinosaurs underwent parental care just like mammals and birds. In the same site Horner also discovered the nests he attributed to the smaller ornithopod Orodromeus. In England great mediatic coverage was dedicated to Baryonyx, a new kind of big theropod totally different to the others, specialized to fishing. While in the other side of the world, the first complete Australian dinosaurs came to light: the most known is perhaps Muttaburrasaurus, and then Minmi and Leaellynasaura. Finally, the Ice Continent unvealed its first dinosaurs: an (for 20 years) unnamed ankylosaurian and an (still-today) unnamed hypsilophodontian, both found in the ice-free portion of Antarctica.
THE 1990s In the Jurassic Park decade the main discover was certainly the first print of feathers found in non-avian dinosaurs, in 1996. Before that, only Avimimus (found in 1980 in Mongolia) seemed showing some proof of feathers, but not prints. Then, Sinosauropteryx and other animals found in northern China changed our perception of dinosaurs, which were much more bird-like than usually thought. Today, dozens of feathered dinosaurs are known, as well as some animals which have had some relation with the bird-dinosaur argument — the alleged "first bird" Protoavis, and Mononykus (which was initially believed a true bird). In North America, the diplodocid "Seismosaurus" competed with "Ultrasaurus" in the early 1990s for the "biggest land animal ever" title; today, both animals are considered invalid by official science. Meanwhile, the traditional "Anatosaurus" was divided into Edmontosaurus & "Anatotitan" in 1990; and then, the discover of Utahraptor upscaled dromaeosaurid size at 7 m of length since 1993. It was also confirmed even Alaska was populated by dinosaurs: the bizarre ceratopsid Pachyrhinosaurus (known since 1930s) has revealed in the 1990s a huge fossil herd near the Polar Circle. Among other continents, South America was particularly plenty of interesting animals: the tiny Eoraptor (long believed the first-ever dinosaur) in 1993, the sail-backed sauropod Amargasaurus in 1990, the nesting ground of Saltasaurus in 1998, and, above all, the incomplete remains of Argentinosaurus (which in turn took over to "Seismosaurus" and "Ultrasaurus" the "biggest ever!" title, now contented by other guys, expecially "Amphicoelias"), and later those of Giganotosaurus (that, together with Carcharodontosaurus, was presented as "bigger than T. rex"; today the record-holder among theropods is officially Spinosaurus). In Mongolia, Oviraptor (better, Citipati) revealed not to be an egg-stealer as traditionally thought. Finally, in Italy, the tiny Scipionyx showed the very-first internal organs in a dino-fossil —- while the alleged "heart" of Thescelosaurus found a bit later in the USA is probably a simple piece of stone casually heart-like.
THE 2000s The New Millennium opened with an unespected find in Northern China: a four-winged dromaeosaurid, named Microraptor, which demostrated once for all that birds are dinosaurs. Later, also in China, some paleontologists started the trend to name chinese dinosaurs with the suffix -long (ex. Guanlong). Meanwhile, the BBC producers popularized some new theories about dino-life thanks to their computer-graphic: rigid-necked sauropods, for example. Other theories emerged from CGI studies include: non-headbutting pachycephalosaurians, non-killing-in-pack dromaeosaurids, non-quadrupedal prosauropods, and so on. Today, the biggest interest about dinosaurs regards their skin: it seems not only theropods but also herbivorous dinosaurs had some sort of feathers or feather-like structures: the quills on Psittacosaurus, the bristles of Triceratops, even the fleshy spikes of Diplodocus could have had the same origins of theropods' feathers, as (maybe) definitively demostrated by the discover of Tianyulong. Not forgetting that one close dinosaur relative, the pterosaur Sordes, had revealed signs of hair-like things already in the 1970s. Talking about pterosaurs, they too have undergone a "renaissance" since the Seventies: the huge Quetzalcoatlus and several other kinds (Dsungaripterus, Pterodaustro, and many others) increased greatly the known ptero-variety, demonstrating "flying reptiles" being as diversified as modern birds in ecology, and as efficient as fliers. While the 1 ft long Lagosuchus (found in the 1970s in Argentina) has demonstrated the evolutionary link between pteros and dinos. About other Mesozoic reptiles found since the 1970s are worth of note the marine plesiosaur Kronosaurus found in Australia, the huge ichthyosaur Shonisaurus found in North America, and the giant crocs Sarcosuchus & Deinosuchus, maybe able to transform large dinosaurs in their meals.
And then, the non-stock dinosaurs divided in subgroups according to their real affinites and sometimes to their external appearence.