I'm no expert, but look up early blight. I'd remove the leafs

I've the exact problem. Can Confirm, as secretmail021 has identified, it is a very very very small insect. White-green color, approximately as wide as 1-2 human hairs, about 1.5 mm in length... you won't see them on the leaf, Instead, pick a leaf and shake/tap it over a well-lit preferably dark surface.... if they fall off, you can see them crawl. Happened with indoor potted plant that was otherwise healthy for the last month. No idea for the solution, but act fast, because it spread from a few just a few leaves to a few plants over the course of half a week. RIP basil.

Blight??? http://www.thriftyfun.com/tf255431.tip.html

These kind of look like Minute Pirate Bugs but are significantly smaller. They jump when touched and I'm almost certain they're responsible for the deadening of my plants. Leaves that are devoid of them are healthy and green. There are hundreds of them on each plant. I spent hours trying to figure out what they are with no success