I think I had that problem with my cucumbers before, and I'm not sure but my best bet would be it's downy mildew..
Nothing is 100% effective on this disease except for preventing it from happening at the first place. You just wait until the cucumbers will die, and I'm not sure but I heard that if you'll apply a copper based fungicide on leaves it'll help, but it'll only slow it down a bit and not completely stop it.

Snip off the worst, try some fungicide, and try to water from underneath. My cucumbers had this last year, and for some crazy reason they didn't die until the end of the summer! I've seen pictures of some other gardeners' and mine never got that bad, it only affected the leaves. My plants were hideous, but they kept producing, which makes me think it may have been a different strain of downy mildew? I had a ton of huge cukes. This year I started spraying since the first pointed leaves appeared...there are a few spots, but I hope those are just bugs.

I'd say it's angular leaf spot. This isn't such bad news as downy mildew.

Maxim's advice will work with this disease, too. Copper fungicide is recommended.