A friend of mine started having plumbing problems last year and decided to check out his crawl space. After a little moving around under the house, he discovered that his house was built in two sections. The first house was built with a rock foundation probably in the late 1800's and was doing fine. However, the other end of the house was sinking into the ground as the floor joists rotted on the ground. He had no foundation on one side of his house; they just laid out the floor on the ground! He's in construction and excavation, so he did what no rational person would do and tore up his kitchen floor so he could have more access and started digging. He started with a fairly small section and added rough-cut 2x8x8s as he went down. Eventually he got to about 6'6" down, then started expanding, hauling all the dirt out by hand in five gallon buckets. I've helped him on a number of occasions and 18 months later, he as the entire north side of his house excavated, he's jacked the house back up with several 15 ton jacks, and put a treated lumber foundation under it. He now has a good sized (~20x16') area dug out and I'm planning on using it as a cache if I ever need to relocate.
Anyway, the biggest lesson I learned was that origionally he was just planning on going down 3-4', but working bent over was so difficult that it was actually less work to take out more material and go deep enough to stand upright. Make sure you're shoring up regularly to prevent cave-ins. Also, it would probably be a good idea to test the crawl space for radon before you start working down there, as otherwise you may be putting yourself and your family at risk.