Orchestras without conductors

There used to be a time when orchestras didn't have a conductor. This was primarily before the early 19th century, so Baroque / Classical. One reason was that compositions were typically not as complex as the more modern ones, so the principal violinist or keyboard player could guide the orchestra pretty well.

For example, this could have happened for Vivaldi's "Four seasons" and some of Mozart earlier violin concerto's. When Beethoven started writing more involved symphonies, the role of a dedicated conductor became more apparent.

Beethoven himself was found on stage conducting his own works, but due to his oncoming deafness, he was often off by two measures.

Another factor is the growth in size of orchestras. It becomes harder for a violinist to keep track of everyone and every part. A dedicated person to look at is just more convenient for everyone.

Interestingly, there are quite a few famous composers that also conducted their own works, such as Mendelssohn, Wagner, and Brahms. The role of the conductor only became more prominent as the 20th century progressed.