I am putting a bathroom in a section of the house that has a crawlspace under it. The main drain is in the basement area of the house. The soil pipes will run horizontally in the crawlspace, then a double 45 to drop down the basement wall, and then horizontal again to run under the floor to the main drain. At the point where the waste line transitions from horizontal to vertical is a vent required? I think I remember reading somewhere that all vertical stacks have to be vented.
No, vents are not required for any random vertical drop. Only plumbing fixtures require vents.
The main point of the vents in the drain system is to let the air enter the pipes at the spots where water enters it too. Without vents two things would happen: First - poor drainage, as both water and air are competing for space in, say, your sink drain. Second - low pressure in the pipes, created by water draining through one fixture, might suck in water from other fixture's trap. Which would let nasty sewer gases into living quarters.
As there's no new water entering at your vertical drop, a vent there won't do anything at all.