First, visit this video on Youtube (sorry, embedding has been disabled). It shows Herbert von Karajan conducting Beethoven's Symphony No. 1 in C Major with, I believe, the Berlin Philharmonic.
It is one of the few Beethoven symphonies that begins with a slow introduction. Though his music isn't far from the classical stylings of Haydn, at this stage, one can already hear a difference, or the beginnings of a difference. It is immediately stamped with Beethoven's assertive personality, sense of humor, and flair for harmonic surprises. The first surprise (or perhaps joke), for those who have ears to hear, is that it starts in the "wrong" key and draws several red herrings across the trail before reaching the movement's tonic key of C.
Quite soon the opening Adagio molto (very slow) gives way to the first movement's main section, marked Allegro con brio (fast, with spirit). Its first theme chuckles gaily, pausing for breath a couple of times before bursting out into unrestrained laughter. An aggressive transition passage leads to the sweet, graceful second theme, introduced by oboe and flute. The exposition's codetta is based on these themes in reverse order. In the development, Beethoven modulates through several keys while messing around with the first theme. At about 5'15" (per Karajan) a blaring horn brings an unexpected moment of gravity to the number. Soon afterward the recap begins, following classical order. Inevitably, the transition passage has been rewritten to keep both themes in the tonic C major; the new transition has a much sunnier outlook. At 7'25" Beethoven eases into a coda that threatens, for a moment, to become another development section. The closing chords are very emphatic.
Movement II is Andante cantabile con moto, which is to say, a lyrical slow movement at a somewhat brisk walking pace. Its lilting opening theme seems, at first, apt to become a fugue subject. Then it turns out to be only the first leaf of an album of charming melodic vignettes. It's one of those movements where all the ideas work together so well that they seem inseparable, inevitable. After hearing it once or twice, one might be able to hum along with the whole thing.
Movement III is a "Menuetto" that really should almost be called a Scherzo; it's that fast. Its main theme races upward like a rocket. Listen for aggressive accents, chromatic ratcheting-ups, rhythmic changes, thundering timpani, and an unsettling alternation between major- and minor-key versions of the same musical gesture: all touches prophetic of the later, maturer Beethoven. The Trio features the woodwinds playing repeated notes against a swirly background of strings. Miraculously, Beethoven makes this immaterial material sound noble and thrilling. The main section of the minuet returns, as any fan of Haydn's symphonies would expect. I particularly like the crescendo at the end.
The finale, like the minuet, is marked Allegro molto e vivace: really fast and lively. It begins, however, with a slow intro of its own. First there is a loud, ominous unison note. Then the strings make several tentative attempts to play a C Major scale, each time getting a little closer to pulling it off - sort of like the lead-in to the Sound of Music song "Doe, a deer." The beginning of the Allegro happens to begin with that completed scale. Boy, does this movement move! It cooks along with a stupendous masculinity, qualified only by its relatively dainty second theme. In spite of its fleet-footed frivolity, Beethoven manages to inject a certain degree of revolutionary humanism into it, courtesy of the brass and timpani. Who knew that you could have comic opera and a triumph of the human spirit at the same time? It's another discovery that characterizes Beethoven's composing career. The joy is scarcely diminished by a couple of minor-key moments in the development. The recap ends on a dramatic, dominant cadence, setting up the coda in which the opening theme hesitantly comes out for a bow before a horn-and-woodwinds passage in which Beethoven seems to say, "Ha, ha! I've made a symphony!" The rest is closing chords.
Beethoven's later symphonies move beyond "Haydn Plus" into the vaster proportions and the more strongly marked, individual style for which he is famous. Nevertheless, the First Symphony reveals early foreshadowings of his later innovations. Above all, it combines the great one's strong temperament with his typical sense of humor and a gift for uplift. Since 1800 it has been guarding the turning point between the classical period in Western Fine Art Music and the romantic era that followed it. From the one side it appears revolutionary, from the other primitive and simple. But from the timeless perspective of another age, it is simply a piece in which we find a 30-year-old Beethoven enjoying himself, and allowing himself to be enjoyed without trying to prove, or demolish, or recreate anything. And that's a gift of its own kind!