German, Austrian and Italian composers dominated the baroque and classical eras of Western music, which is what is commonly thought of when we think of "classical music" today. However, in the early modernist era of the late 19th and early 20th century, the influence of composers from other areas of Europe cannot be ignored. For example, French composers like Claude Debussy and Maurice Ravel were crucial to the impressionist movement around this time, and Englishman Edward Elgar wrote many works which are considered standards today, such as The Enigma Variations and the Pomp and Circumstance Marches. Meanwhile, Charles Ives of New England received critical attention for his merging of classical music with American folk sounds, while the Hungarian Bela Bartok's study and elevation of traditional Hungarian and Eastern European folk helped influence modern Ethnomusicology. These are just a few examples out of many composers of the period from all over Europe and North America.

My answer is going to focus heavily on the 18th Century for the first part, in which Austro-German and Italian composers are by far the most widely played. After this I'll discuss the 19th century into which some Russian composers and other Eastern European composers come into play.

The use of "popular" in your question really defines your answer. Music suffers heavily from a teleological approach to historical studies, resulting in what has been referred to as the mainstream musical canon (or imaginary museum, to use Nicholas Cook's term from "Music: A Very Brief Introduction" which gives a great insight into many areas of musical study).

This approach to studying music did not come about purely by accident but was a result of a number of factors, both musical and socio-political. Music in the Austro-German tradition tended to concentrate heavily on certain aspects of music, including but not limited to form, harmonic progression and, in a more abstract sense, appealed to the values of the imperialistic societies of its time. Charles Rosen makes a good job of analysing music of the 18th and 19th century in this style in his renowned book "The Classical Style". However, in a way, books like "The Classical Style" only serve to further the canon even more into the 21st century, but I'll talk a little about that in a minute.

However, even though German music was more highly valued than the "popularist", melodic, Italian music (perhaps because, being mostly instrumental rather than operatic, it was seen as timeless, rather than an aging reflection of the times) you're quite right in saying that both traditions from the 18th century enjoy far greater popularity today than music from other places. This comes down to a couple of things; both countries were the among the first to widely accept the tonal system made popular around 1730-1750. Retrospectively, this caused historians and musicians alike to gravitate towards using them as musical examples, and ignore composers who used musical methods that ended up in a historical dead-end, so to speak. It also cannot be underestimated how much of a cultural centre Vienna was during this time, and to a lesser extent Italy too. Vienna, in particular, had the double-whammy of being known as a centre of Enlightenment and haven for the arts while at the same time being under the strict rule of the Empire, resulting in free art that was not upset by ideas of Revolution in the same way France was. There's some great contextual details about Vienna, and the wider late-18th century, in Tim Carter's informative guide to the Marriage of Figaro. To name some composers that lived and studied in Vienna: Haydn, Mozart, Beethoven, Schubert. The world was, in a sense, looking to Vienna to produce art rather than looking to themselves, and Vienna gave these composers as payment. Much of the 18th century canon comes down to nations and cities in Europe not wanting independence, but instead wanting to be as fashionable, popular and cultured as places like Vienna, resulting in the glorification of foreign composers over their own.

Much of this changed in the 19th century, though not necessarily for good reasons. Nationalism became extremely important, and remained so until the Second World War, a century and a half later. Nationalism cuts both ways in music. It produced scholars and musicians who regarded themselves as the "next step" in musical history, based on what they knew had come before. Now, the problem is, much of the only accepted music across Europe was Austro-German (as discussed above). This left other countries defining themselves against this culture, the mainstream, while composers from this culture were free to define themselves as "the norm", the good, the superior. There are many, many books on musical nationalism and I won't pretend I know them all - but I do know a good book analysing it and studying it impartially is Edward Said's "Orientalism". The situation of the musical canon now sits firmly in the hands of the Austro-German. Europe looks to them for inspiration - either producing composers that write in their style or composers who aggressively do not write in their style. However, the only composers that are well-known today are those who wrote in a German style with inflections of their own "folk" traditions - such as Tchaikovsky, Dvorak and, later, Sibelius. For an Austro-German audience, they saw something exciting and exotic that did not threaten their cultural dominance. Today, musical repertoire is comprised still mainly of what the Austro-German canon was at the end of the 19th century - German-speaking composers (Wagner, Liszt, Beethoven, Mozart, Bach, Haydn, Schubert, Schumann, Brahms, Strauss etc) and German-style exotic composers (Berlioz, Chopin, Mussorgsky etc).

Modern musical texts, generally, do not help the situation even while accepting that the society-created canon of "good" works still exists. For example, Richard Taruskin's monumental "Oxford History of Western Music" does a very good job of describing the canon, its faults and causes - before going on to describe the history of those composers contained in it anyway instead of concentrating on bringing all elements of "Western" music to study, not just the famous ones.

However, it's not that there is a lack of sources for contemporary music to "the greats" that can be studied and played. I have personally worked with a publishing company called INTRADA that specialise in finding music written at the same time as composers mentioned above, particularly in the 18th century, but written in a different musical style. These pieces are then published and recorded - but, they never make it too far into mainstream repertoire, perhaps because modern audiences are content with the security they have in their model of history and wouldn't benefit from shaking it up.

I hope I have answered your question. The popularity of the mainstream canon, which we still listen to today, comes from a variety of reasons centring around the cultural hub of Vienna, and national reactions to German music in the 19th century. I'm going to write, for a paragraph or so, about the 20th century below because it provides a really interesting counterpoint to the canon.

During the 20th century, nationalism became its most powerful, producing composers like Schoenberg who believed he had perfected the Austro-German tradition, and analysts like Schenker who tried to prove German superiority through complex analytical methods. This, of course, tied very neatly in with the fascist government that arose before WWII. To a lesser extent, the same happened in Italy under Mussolini, though composers there were undergoing a little more of an identity crisis, their powerful musical culture having been supplanted by Austria-Germany in the preceding century. This information I have learnt from Richard Causton, an expert in Italian music of the 20th century. After the war, German and Italian composers felt that they needed a break, a "day zero" to quote Stockhausen - where they completely abandoned the technique used by their aggressively-nationalistic predecessors. As a result, the new style of electronic music came into being while other countries remained composing with largely traditional means. I am over-generalising slightly but the core point is true. I find it interesting that German composers shied away from their culturally dominating past, only to create a new style of music that was in its own right extremely influential in the 20th century. But the 20th century is not what your question was about, just a little side-note.