I am putting Downlighting in my basement. Is there a rule to follow regaring how many or how far apart the can light should be?

The fixture manufacturer should be able to supply performance specifications and diagrams for its lighting fixtures. Spacing depends on the lighting level you want to achieve, and the ceiling height.

Downlighting is my least favorite form of lighting. Unless a special fixture is used, it produces glare, and is very uncomplimentary to human beings' faces, and often too many light sources are visble.