I noticed the problem before it got too bad -- a thin layer of water over about a third of the basement, and thankfully noticed it was because the pumps weren't working. I reset the GFI and they started working, then went to damage control in the basement. I spent about two hours last night pushing water around with a mop and a big squeegee and vacuuming it up in my little wet-dry vacuum (maybe I should get a bigger one), which pulled up about 5 gallons of water. Then I set the fans out.
I got up this morning to discover that most of the water was gone, and what was left had collected in an area near the far corner. I moved the fans over there and spent another half-hour or so vacuuming up water (about 3 gallons, this time). I moved some of the boxes around so the water that had collected under them can evaporate, too. I'll go back down in another hour or so (Yeah, I took the day off from work -- at least the morning, anyway -- so I can deal with this.) and move some more stuff around and see if there's anywhere else I can target for water removal. I'm actually pretty impressed by how much it helps to have those fans working down there.
It doesn't look like any of our stuff is damaged -- it's all in plastic boxes, with much of it up on cinder blocks.
I wonder what caused the GFI to trip? When I reset it last night, in the rain, the pumps came on and started working -- it didn't immediately trip. It's been fine all night -- the pumps were still working when I woke up this morning. I guess we'll just have to get in the habit of checking the GFI at least once a week, and definitely when we know it's going to rain.
Our window wells do have drains in them, but they're obviously clogged -- and have been for quite some time, since the previous owner decided that installing a pumping system was a better solution than depending on the drains in the window wells.