Beethoven is great, in my opinion, because of his character, his humanity, which shines throughout his music. Whether he is considered a classicist or a romanticist, he wrote in a most unyielding, unpretentious fashion. His individuality is his greatest contribution to music.
To answer the question simply as a music lover, I think Beethoven's symphonies are his most "influential" works. These are the most iconic classical pieces that I can think of. They define classical music. And by the way, didn't Wagner have the 9th in his mind when he started off his enterprise of "musical drama"?