There are different schools of thought on whether or not this is the right way to go, but Catherynne M. Valente is publishing her novel chapter by chapter here online, with a facility for donations. I haven't yet read the first chapter, but the first sentence is very promising: "Once upon a time, a girl named September grew very tired indeed of her father's house, where she washed the same pink and yellow teacups and matching gravy boats every day, slept on the same embroidered pillow, and played with the same small and amiable dog."
And she's not alone. Freely available children's fantasy short stories can be found here.
Of course, the problem is, if we all get used to free content, how will the writers be paid? Will opportunities to be full-time writers dry up? Will what is effectively busking online really generate income?