Some of you may be groaning already, but I had never heard this before. Evidently, a number of people over the years have speculated on Beethoven's ethnicity. I think it's pretty clear he wasn't 100% of African descent, but the most realistic speculation is that he was a "mulatto", to use the parlance of the time.
This page gives many interesting quotes and tidbits to back up this claim (none of which I have the time to independently verify in any way), including this one which is interesting:
In speaking of the immortal Haydn who was Beethoven's teacher, Andre de Hevesy, says: "Everybody knows the incident at Kismarton or Eisenstadt, the residence of Prince Esterhazy. In the middle of the first allegro of Haydn's symphony, His Highness asked the name of the author. He was brought forward. "'What!'exclaimed the prince, 'the music is by this blackamoor? 'Well, my fine blackamoor, henceforward, thou art in my service.'"
Here, however, is a pretty stern refutation of this speculation, claiming that Beethoven's lineage is well-documented (but giving no references as such).
Given the aforementioned evidence, I think that I can say with 100% confidence and accuracy: Beats me.
On a more perplexing note, some are ruffling feathers by asking an even more provocative question: Was Michael Jackson black?