Can make things a lot better in my opinion. I've had monster hauls of perch on rainy days, one day when I was a kid it was Peeing down all day and we didn't stop catching the stripey buggers and had our fair share of Pike on spinners too.
I also find slightly overcast days tend to be a lot more productive when fly fishing for trout, usually best when there is some sunshine and showers. It breaks up the day a bit and tends to turn them on to feeding when the cloud comes overhead, perhaps the old "fish dont have eyelids" factor comes into play as they can maybe spot their prey better without the sun glaring on the water.
Obviously look out for lightning when holding 8 or 9 foot of carbon in your hands but otherwise I say FISH ON! As long as you have some decent wet weather gear to stay dry and comfortable then you'll be fine.
The fish are wet already, they dont care.