Absolutely! Depending on what you think of as a hit, there are songs stretching back to the Middle Ages at least that can be considered incredibly successful. (Note that all of these examples are from a Western canon – to its considerable detriment, music history is generally taught almost exclusively from a Western, Eurocentric perspective in Europe and North America. I wish I had examples to suggest from elsewhere.)

Musicology tends to – somewhat contentiously – draw a distinction between folk music (without known author and orally transmitted from musician to musician), art music (composed, originally, for wealthy patrons or the church and connecting to a certain orchestral tradition) and popular music (written for commercial purposes and transmitted through media.) However, it can sometimes be hard to delineate cleanly between them. We live in a thoroughly mediated age, and have for many centuries, and the cross-influence of printed and later recorded media is difficult to discount, even with supposedly pure folk songs and art music compositions. Especially when looking at the idea of something becoming popular, it is important to bear in mind just how much printing and dissemination via commercial sales impacts this.

When collectors started collecting traditional folk music in the 18th and especially 19th century, they would travel among communities across mainly Europe and North America and try to find songs that had been passed down through generations. Some of these turned up again and again, may going back centuries – but some certainly not. In the UK and Ireland, the song that got collected the most times was undoubtedly "Barbara Allen", a folk song that enjoyed widespread popularity as an orally transmitted piece, but also one which was originally written by a specific, now lost songwriter in the 17th century, performed from the very beginning in theatrical settings and printed in collections and on broadsides over and over again during the subsequent centuries.

This is one possibility of understanding of what a hit song is – a song that has become widely disseminated through a mixture of oral and mediated transmission. Unlike today, it would not be connected to a specific performer, but they could still make their creators rich – broadsides would sell hundreds of thousands of copies a year by the late 17th century, and once bourgeois, home musicianship became popular during the Victorian era sheet music would create huge hits in the same way recorded music later would. Songwriters like the American Stephen Foster (1826-1864) would have enduring hit upon enduring hit, in the form of songs disseminated by musical troupes, vaudeville and (more unpleasantly) blackface minstrelsy groups, and then ending up as sheet music in homes in the hundreds of thousands of printed copies. (Some Foster songs that still live on today include "Oh! Susanna", "Beautiful Dreamer", "Camptown Races", and "The Old Folks Back Home"/"Swanee River".)

On the art music end of the scale, the 19th century saw a huge shift away from art music being for a narrow elite and into much more broad popularity. Performers moved from genteel courts and restrained cathedrals and into huge, sold-out concert halls. People like pianist/composer Franz Liszt and opera singer Jenny Lind were as popular in their day as rock stars are today, with massive crowds gathering both inside and outside venues, people fainting and screaming, the whole deal. (The fact that they were both attractive definitely helped, as with today's artists.) Suddenly, composers found their works performed and disseminated much more widely, and certain pieces definitely became hits in the sense of having many different ensembles play them, across the Western world. An opera like Verdi's huge hit Rigoletto was performed in many dozens of cities by different groups in the years after its 1851 Venice premiere, to take a popular example.

As for novelty hits, there were certainly many in the printed sheet music industry – humour was and still is a big seller in music. But if you want something that had to be seen live, how about Tchaikovsky's 1812 Overture from 1880, a very popular and often played art music piece? It is composed to include a battery of artillery cannons (!) that fire sixteen times at the climax of the performance. Can any contemporary pop hits top that?

Sources:

Roud, Steve & Julia Bishop (2012). The New Penguin Book of Folk Songs.

Linkon, Sherry Lee (1998). “Reading Lind Mania: Print Culture and the Construction of Nineteenth-Century Audiences.” Book History 1

Walker, Alan (1987). Franz Liszt, The Virtuoso Years (1811–1847) (revised ed.). Cornell University Press.