Hello to scrapman & all other Forum Memebers,
I think that the other Forum Members pretty much covered all of the basic ways to remove tires from the rim's. You can definitely do it by hand without a tire machine but without the actual tire bars it is somewhat hard, but it can be done. Last week our loader got a flat and we were able to pull the tubless tire off the rim and patch it, all by hand, however I do have the proper tire tool / bars.

As far as regular truck and car tires go these days, we now use a simplified method for tire removal (see photo's) It not only cuts the rubber tire right off, but also cuts the steel rim, but with bigger truck tires you have to turn it over and slice it a second time if you want to cut the rim in half.
The big draw back is safety issues, I realize that we need to fabricate a safety guard. I would venture to say that it is probably the most dangerous equipment we utilize.

I should also say that the vast majority of the Shear use is for cutting / prep- steel, it saves a tremendous amount of time & torching.

The following is the shear photo and our flat tire:

http://i1209.photobucket.com/albums/...11/Shear-1.jpg