Beethoven's influences were many. I think the largest influence on Beethoven was the two time periods he straddled. Beethoven was heavily influenced by the Neoclassist perfectionist style we see in works of Mozart and Haydn, but he was also a product of the Romanticist age. In some respects, Beethoven is a natural extension of both and a figure that unifies both periods of intellectual and musical history.
Beethoven is a product of a moment in time that has a hold in two particular intellectual traditions. In terms of the influence of Neoclassism on Beethoven, one can see this in his technical proficiency and elaborate, ornate style in many of his works. His piano sonatas ("Fur Elise" and "Pathetique", for example) reflect this intricate and technically demanding notion of perfection in work. Like Mozart, Beethoven believed that the patronage system, which was evident in the Neoclassist period, had its limits and that the artist had a devotion to perfection in his craft. It would be here where we begin to see his emergence into a Romanticist philosophy that demanded that the artist is individually distinct from society, attune to a level of perfection that only they can attain. This distance might have also been enhanced by Beethoven's deafness, which caused him to retreat even more into a world that only he could perceive and understand. Along with this influence, the revolutions of 1848 and of the time period had a profound influence on him. He devoted his Symphony # 3 to Napoleon, as a representation of his love of the spirit under which Napoleon ascended to power. Yet, he was dismayed at his autocratic ways, and rescinded his dedication. The Romantic spirit can be lucidly seen in no other place than in his Ninth Symphony, inspired by Schiller's poem "Ode to Joy." Originally conceived as a type of masterpiece, this particular symphony captures the intensity, pain, and glory of the feel of revolution on political, spiritual, and artistic levels.