Now I know this is dependent on the PC to a big extent but I've been out of the loop with modern hardware for a few years. I have a project where a large 3D texture might solve things, we're talking maybe 512^3 but probably 8-bit, single channel. Memory wise this is not a big deal (it's not a game project and there are not lots of models or textures in use) but I really don't know if it would be supported on a typical PC (not a games rig). Or if it would slow things to a crawl... or once it's in the GPU memory it would not be unduly performance-limiting?

the maximum size of a 3D texture in D3D11 hardware must  is 2048 (on all axis, so total maximum resolution can be 2048*2048*2048). so yes, it is supported on virtually every hardware out there. Performance wise there shouldn't be a difference that a 2D texture

Under OpenGL, this limit is defined by querying GL_MAX_3D_TEXTURE_SIZE. Also, as stated here, try to stick with POT texture sizes as much as possible.

To my opinion, the API will never give a size that, when used, will make the texture unpracticable (ie, too slow to be rendered or to be probed in a shader).