I think it's called 'White Slime Mold', but I suppose it could be a number of things.

Yep, we went from drought to flooded basements. So much for moderation.

I signed up to GardenWeb just a few minutes ago because I was going to ask the same question and came across this post! I am in Eastern Tennessee and today we found a material on our cucumber plant, very similar to what is in the photo, with little insects walking around covered in it! Was wondering what it is and what type of pest the insects are. When I try to touch one they hop from leaf to leaf. It is mainly concentrated on the stems of the fruits.

There are a couple of insects that have that white, fuzzy characteristic. The few that come to mind are mealy bugs, wooly aphids, and white scale. I don't think they are too problematic outdoors. If you do a search for each one of those you can find some info about getting rid of them. Sometimes just cleaning the stems off works fine, then the good bugs can get to them without the fuzzy stuff in the way.

I think there's a leaf hopper nymph that is fuzzy also, but I'm not sure it makes stems or leaves fuzzy.

The white substance in the photo is just the visible signs of a fungus. Fungi are the primary digesters of organic matter and they are working on breaking down the wood in the mulch. Moisture, including several days of rainfall, just encourages the production of the fruiting bodies (reproductive means) of these fungal organisms. They are almost always harmless to plants.

Without a photo to illustrate, it is impossible to say what might be up with G&G 1974's cucumbers. But cukes and other members of the cucurbit family (squashes, pumpkins, melons, etc.) are extremely prone to powdery mildew, which often produces a dense white fuzzy substance. That CAN be an issue with the plants and needs to be controlled. But that is just a guess without any visual confirmation :-)

Thanks for the responses. I was wondering if I need to deal with it, if it's harmful to my ground cover and if it's harmful to pets. I'll do a little more research. Thanks again.