Oeuvre
For finales, the meteoric fugue which ends the Quartet #9 (3rd Razumovsky) beats everything. For sheer wildness, the "Grosse Fugue" (originally meant as the last movement of Quartet #13) deserves special mention.
I listed single movements because even Beethoven doesn't maintain the same stratospheric level of inspiration through every movement in most major works --- although he came close enough in the quartets #7, #8, #14, and #15, and the Symphonies #3 and #9, and some of the piano sonatas.
What strikes me about Beethoven is how many of his works are wonderful, including many that are less intense than the ones cited. There are all kinds of genial Beethoven works that knock one out: the symphonies #2 and #4, the Violin Concerto, the 4th Piano Concerto, the "Diabelli" and "Eroica" Variations, the "Consecration of the House Overture," and the String Quintet in C.
I also like the unassuming "Creatures of Prometheus" and "Ruins of Athens" ballets. I am even fond of the dopier occasional pieces, like the "King Stephan" and "Wellington's Victory" overtures. In my dotage, I have been acquainting myself with the whole of Beethoven's oeuvre, and, as with Bach, there are hardly any weak spots.
This question led me to go down to the basement to poll my CD collection for composer representation. Bach leads them all handily, followed by Beethoven. The next are Shostakovich and Vaughan Williams, who are tied for 3rd place, followed by Brahms, Sibelius, and Hindemith tied in 4th place; then Dvorák, Rachmaninoff, Bartok, Vagn Holmboe, and Einojuhani Rautavaara ... essentially tied in 5th place.
One of my friends once chided me for snubbing Dvorák in our youth. Something must have changed: We all start to go a little soft in the head with time. I even have a fair amount of Tchaikovsky now, less than Stravinsky, but about the same amount as the Oyster Band.
If you want to look into less familiar Beethoven chamber literature, I recommend the following. Among the string quartets: the Opus 18 #4 in C minor --- an early ripsnorting romantic work --- and the quartet #10 Op. 74, in E flat: a fine, lyrical piece that has somewhat gotten lost between the dazzling Razumofskys before it and the visionary late quartets after.
Then, the mysteriously under-appreciated string quintet in C, Op. 29, a very melodious work that sounds more like Schubert than LvB; the genial Serenade for flute, violin, and viola Op. 25; the C minor string trio, Opus 9 #3 --- another early ripsnorter --- and the magnificent 'cello sonatas # 2 and 3.
We associate the Romantic movement with the 1800s, but Beethoven wrote the two intense, emotional C minor pieces listed above in the 1790s. In fact, the Marquis de Condorcet is said to have coined the word "Romanticism" in 1793 to describe the music of Nicholas Mehul, who was seven years Beethoven's senior. He was a well-regarded young composer during the last days of Louis XVI, but did even better after the revolution ... although one of his unfortunate teachers lost his head in the Place de la Republique.
Mehul churned out a huge number of revolutionary operas for the Opera Comique, became Napoleon's favorite composer during the Empire, and finally adapted successfully to the Bourbon restoration in 1815 (although he died two years later). His music is colorful and melodramatic, although not particularly innovative at the deep level of Beethoven's music. It sounds about midway between Mozart and Berlioz ... and is rather a gas, though certainly not in the master's league.