Here are four selections from Fabeloj de Andersen (link); only the four under Fabeloj kun Voĉo have sound, the rest are just text. There are some others on LibriVox, but the pronunciation isn't very good. Like sometimes pronouncing "c" as "k" and stuff.

On the other hand, the LibriVox reading of Alicio en Mirlando, linked in another answer, is well-done and quite pleasant to listen to.

Looks like most of the rest of the Esperanto material on LibriVox is individual selections from multilingual poetry collections, and some other bits of this and that. One of these days I'll get a computer that doesn't drown out my voice with its CPU fan, and then I can help get more recordings out there...