I have some really old movies I'd like to convert and be able to watch. Does anyone have any idea how to get them converted to a current form of media like CD, DVD or even VHS? Right now they are 8mm Kodachrome films.

There is little scope of answering this question in short. If you are planning to do this yourself you will need:
a) a good DV camera
b) the same number of hours as the amount of footage you have
c) a "Telecine" unit - a very very basic one will cost close to $1000/-
d) you can try without (c) by projecting a very small image on the screen and using your DV camera to record off the running movie. Will require a lot of trial and error with the angle of the camcorder to get even a passable quality of DV footage.
e) Then transfer the DV footage to VHS, CD or DVD.

Try googling Telecine.

I had the same problem. I found that I could shoot a video of the film by putting a video camera on a tripod and rephotographing the film footage projected on a white wall. Not great quality, but acceptable, and it's very cheap. Also, you can turn the video cam on and off to get just the parts you want. Of course, it means you have to have a projector. If you don't, I imagine pawn shops should have them for a small price.

Depending on how much footage you have I would pay for the conversion. Most photo processing places will do it for a cost per foot of or hour of film. Its not that expensive and the quality of the conversion will be much better.

I had the same problem. I found that I could shoot a video of the film by putting a video camera on a tripod and rephotographing the film footage projected on a white wall. Not great quality, but acceptable, and it's very cheap. Also, you can turn the video cam on and off to get just the parts you want. Of course, it means you have to have a projector. If you don't, I imagine pawn shops should have them for a small price.

It is the only cheapest alternative. But you actually need to give the same amount of hours as the film length. Then you also face the problem of frame rate conversion because the 8mm projector will be running at 16-18 frames per second and your DV camcorder at 30 or 25 frames per second (depending on NTSC or PAL).
If you can afford and if the clips are really valuable personally - go for a professional.

Check a nearby service to do your transfer.
Try here (http://www.retiredfilmguys.com)