"Das hindert uns, in so naiver Weise ein "verwaschenes Modell" als Abbild der Wirklichkeit gelten zu lassen. (...) Es ist ein Unterschied zwischen einer verwackelten oder unscharf eingestellten Photographie und einer Aufnahme von Wolken und Nebelschwaden."
Classic papers on quantum mechanics and its interpretation
There were essentially two routes to quantum theory, one by statistical mechanics and the other by spectroscopy. The famous piece Planck (1901) introduced the quantized action to account for the radiation of a black body. This line of thought was further developed by Einstein (1905) in his Light-quantum paper. On the other hand Bohr (1913) tackled the question of spectroscopy.
In 1922 Otto Stern and Walther Gerlach discovered what became known as spin - truly the prime example of a quantum property! However, at that time it was interpreted as evidence for "space quantization" of the orbital momentum. (For the anecdotal part of this discovery see here. There you learn for example that cigar smoking played a major role in the discovery and that every time you are shopping at a Woolworth store you have reason to think of quantum mechanics!)
Contrary to popular belief, the notion that the world is indeterministic was already arround before the advent of quantum mechanics. Erwin Schrödinger, in his inaugural address at the university of Zurich delivered on December 9, 1922 (and published 6 years later in "Naturwissenschaften", Heft1, 1929) argued for the statistical character of physics laws. His later development of wave mechanics was inspired by de Broglie's work on matter waves (e.g. in the thesis from 1925).
However, when Born in 1926 gave a statistical interpretation to Schrödinger's wave equation, Schrödinger himself was not happy (and stayed unconviced until the end.). Note, that originally Born applied his statistical interpretation only to stationary states. It was Pauli who realized that this restriction was not needed. Here is an other paper (written in '27) in which Born discusses the statistical character of quantum theory. Schrödinger preferred the view that the wavefunction represents something "real" and explains this view e.g. in this paper from 1926. However, it was Lorentz who first pointed out to Schrödinger that dispersion would spoil this interpretation. Already in 1926 Madelung (Z.f.Phys.40, 322) gave a hydrodynamical interpretation of the Schrödinger equation which is often cited as a forerunner to Bohm's theory.
However, Heisenberg (together with Born and Jordan) took a different route to quantum mechanics anyway. His paper of 1925 ("Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen", Z.f.Phys. 33, pp.879) together with the piece ("Zur Quantenmechanik" (Z.f.Phys.34 (1925) pp.858.) by Max Born and Pascual Jordan led to the famous "drei Männer Arbeit", titled "Zur Quantenmechanik II", published in Z.f.Phys.35 (1926) 557. This paper is generally regarded as the "certificate of birth" of matrix mechanics.
In this famous piece by Heisenberg from 1927 the uncertainty relation was introduced! This work is based not only on matrix mechanics but owes also something to Schrödinger's wave mechanics and Dirac's work which will be mentioned next:
At this point the patience of the non-German speaking reader is again rewarded, since in 1925 the by then unknown Paul Dirac surprised the continental physicists by his "The fundamental equations of quantum mechanics"(Proc.Roy.Soc.A 109 (1925) 642.). Based on Heisenberg (1925) he could show the close relation between classical Posisson brackets and the commutator relation of quantum theory. The led Dirac to a more abstract reformulation of quantum theory in "On the Theory of Quantum Mechanics" (Proc.Roy.Soc.A 112 (1926) 661.) and "The Physical Interpretation of Quantum Dynamics" (Proc.Roy.Soc.A 113 (1927) 621.) based on the "transformation theory" (which was independently developed by Jordan and Born).
In 1928 Dirac published his "The Quantum Theory of the Electron" (Proc.Roy.Soc. A117 610.) in which the Dirac equation had its first appearance. He could show that the property of "spin", introduced in 1925 by Goudsmit and Uhlenbeck (Z.f.Phys.35 (1925) 618) and incorporated into the Schrödinger theory by Pauli (Z.f.Phys.43 (1927) 601) could be naturally accounted for in his relativistic theory! The negative energy solutions were latter identified with "holes in the Dirac sea" (Proc.Roy.Soc. A126, (1930) 360-365.). At that time Dirac identified these holes with the proton, hence the paper is titles "A Theory of Electrons and Protons". Only in 1931 the anti-matter (i.e. the positon) concept was introduced (Proc.Roy.Soc. A, 133 (1931) 60.).
But back to the interpretation of non-relativistic quantum mechanics which keeps many people busy (until today). An often cited piece on the early interpretation of quantum theory is the Como lecture (Bohr, 1928). The work "Licht und Leben" (Bohr, 1933) contains some more discussion on the infamous concept of complementarity.
It is controversial whether the "orthodox" interpretation has roots in the positivistic philosophy. E.g. Fayne has denied this claim with regard to Bohr. However, at least Pascual Jordan has made this connection explicitly in "Über den positivistischen Begriff der Wirklichkeit" (1934). This work by Frank (from 1929) expresses the same attitude.
An interesting spin to the foundational debate was given by the Einstein, Podolsky and Rosen paper (EPR) in 1935. However, it is widely believed that Einstein's main argument did not come out properly. But the reply to EPR by Niels Bohr is no master piece either. The reaction of Schrödinger was way more fruitful. In a series of papers ( 1.part, 2.part and 3.part) Schrödinger came up (among other - even more important - things) with his famous cat-experiment.
Also Schrödinger remained very sceptic towards the orthodox interpretation of quantum mechanics and published the famous article "Are there quantum jumps" (part 1 and part 2 ). Max Born came up with the following reply. It contains a funny typo (errata from '53).
Another groundbreaking work on the interpretation was written in 1957, namely Everett's paper on relative states. Given its provocative content, his teacher Wheeler seemed to feel constrained to publish the following accompanying remark.
John Bell had some influence in revitalizing the research on "hidden variables". This famous paper was written just before the Bell-inequality was found (however, published only afterwards. Since Bell moved from Stanford to Geneva at the time he did not receive the mail from the journal...). The famous Bell reference is J.S. Bell (1964): "On the Einstein Podolsky Rosen paradox". Physics 1, 195-200 in which the Bell inequality is derived.
A paper that I like very much is Ballentin's work on the statistical interpretation, written in 1970. Some people claim that this interpretation is refuted nowadays, but I can not see how and why. Note, that at that time a publication on the interpretation of quantum mechanics was accompanied by a remark on the editorial policy.
Finally, Ghirardi, Rimini and Weber (GRW) gave a specific answer to the question whether there are quantum jumps.