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I've been extremely intrigued by these 3D printers that have become available for consumer use. I'd really like to one day see what they can do. If I were interested in getting started in learning 3d design on my own, where would I start? I figure I might want to eventually take some online courses or perhaps an on campus one at my local community college. Any advice would be much appreciated.

Have you tried downloading Blender? It's free, and it doesn't get much better then that. There are no shortage of free tutorials to teach you how to use it, as well.

Autocad also has 123Design, which I am less familiar with but looks equally free.

Also, Google Sketchup.

Once you have the files made, you can upload them to Shapeways, and they will print them for you in high quality. At that point you can recast your master and produce your models.

Seconding Blender. It's worth learning to use a proper editor instead of Sketchup, which is an absolute nightmare to use (at least, if one's used to working with the amenities a full editor provides).

I don't know if it's mentioned in Ouze's link, but there's an extremely comprehensive wikibook on Blender as well.

Getting a program like 3DSmax, Maya, or Blender, and just playing around is a good way to start. Do some tutorials, get comfortable with the environment.

For modelling, it's incredibly important that you learn how to properly manipulate geometry to be efficient and aesthetically pleasing.

I would also recommend learning how to draw, or at least the basics of drawing. Things like perspective, geometry, and anatomy are incredibly important.
To give a little context, at my university, I major in New Media. A major aspect of that is videogame design/production. Of the lot of them, I was one of the very few who also took a lot of traditional art classes and did any actual life drawing.
Now, 3D modelling is not something I came to particularly enjoy, so I stopped doing it shortly after I tried it, but even then, I managed to be a far better modeller than the people who simply took the technical modelling classes and aimed to turn it into a full-on career (for what it's worth, most of the modellers I studied with were not any good), simply because I knew how the forms I was modelling actually looked.
If you want to be good at modelling anything, you'll have to look at your subject in the way that any traditional artist would. A strong theoretical understanding will get you a hell of a lot further than knowing all your hotkeys.