So far so good. My basil is happy on my balcony and offering its spicy leaves for my tomato and mozzarella salads this year. I haven't heard of the downy mildew fungus hitting Oregon yet, but it's making its way up the east coast, through the Midwest and into California (what doesn't find its way to California?) Growers are the ones getting hit with this the worst since it's a community disease that spreads faster than a cold on an airplane.
I've been inspecting the basil regularly and looking for yellowing on the top of the leaves and gray specks (the spores) on the leaves' undersides-again, so far, so good. Not sure why I'd be getting it first but stranger things have happened. If you do find it pull the plant, isolate it and toss it in the trash-don't put it in the compost. Try not to shake the crap out of it when you remove it-this goes for all weeds and plants going to seed or those that are affected by air-borne diseases. You'll want to keep those seeds and spores on the plant and not in the air where they're going to work their magic all over again.
Keep the basil in full sun with good air circulation, regular water; you know the drill. Let's hope the dreaded fungus doesn't like Oregon as much as the hipsters do.