Beethoven composed nine completed symphonies. They form one of the central achievements of the orchestral repertoire, tracing his development from the elegant Classical style of Haydn and Mozart toward the larger, more dramatic sound of the Romantic era.
His First Symphony premiered in 1800, while the Ninth was first performed in Vienna on 7 May 1824. The Ninth is especially famous for adding vocal soloists and chorus in its final movement, which sets Friedrich Schiller's “Ode to Joy.”
Beethoven did begin work on a Tenth Symphony, but he died in 1827 before completing it. Sketches and fragments survive, yet they do not count as a finished symphony. That is why the accepted answer remains nine, rather than ten. The numbering also excludes other orchestral works, such as the Choral Fantasy, that are not formally symphonies.