Aaron - what is the foundation made of, and do you know what type? Where is the water-table in the area? How is the condition of the foundation? All of these are pretty important questions... Most foundations (in my area at least) are called "strip footings." This is basically just a block of concrete poured directly into a trench, so that the weight of the house sits directly on "un-disturbed" soil. If this is the case with your house, then digging the crawl space down is not an issue... as long as you only do it in the center of the space, away from where the foundation is bearing on the un-disturbed soil. On the other hand, bigger buildings tend to be built on caissons with "grade beams" - so that the building itself sits directly on bedrock. As long as the bottom level is not a floating slab, you can dig to until the building is sitting on bare rock and not affect its stability.
In terms of water intrusion... this is related to the water table and grade of your yard (and soil type) more than the crawl space elevation. If you live in an area with a really high water table, so that digging down 6" causes a hole to fill with water, then maybe don't do it. On the other hand, if your yard drains back toward the house, you will get water intrusion from surface runoff. In most cases, water does not percolate very quickly through soil, so a normal rain-storm will inundate the top 6" of soil, and then the rest of the water will become surface runoff, going into rivers and eventually to the ocean. In soils with a high clay content, it can take months or even years for water to percolate even 1" (which is why clay is used to line landfills... keep that trash juice away from me!).
So I guess the answer is... it depends. Stay away from your foundation and any support columns, control water, and generally you will be fine.
