Sure there are 3D fractals, in the sense that a fractal surface can bend and extend out of a 2 dimensional plane. Take for example the fractal "sponge created by iterations of this method:
Starting with a cube divided into 9 congruent smaller cubes, take the 4 cubes that are the center of each face and remove. Now perform the same operation on each of the 5 remaining cubes. Repeat ad infinitum.
You are left with an object in a 3D space, but what is its volume? Well, zero, actually, and this is where your question becomes a tricky one. Does an object with zero volume exist in 3D? This is why most mathematicians consider fractals to have intermediate dimension, in this case somewhere between 2 and 3.
Answered by:
Rob Landolfi, None, Science Teacher, Washington, DC

Broken glass, mountains and human lungs are some 3d fractal examples. Although someone could say that a fractal can not have an integral dimension as 2 or 3, but something in between.
Answered by:
Spiros Besis, M.S.

'The strength and weakness of physicists is that we believe in what we can measure. And if we can't measure it, then we say it probably doesn't exist. And that closes us off to an enormous amount of phenomena that we may not be able to measure because they only happened once. For example, the Big Bang. ... That's one reason why they scoffed at higher dimensions for so many years. Now we realize that there's no alternative... '