I had a mysterious wet spot in my basement, as well, a while back. A very noticable amount of water, about 6 feet from the nearest wall, but the surrounding floor/walls/ceiling were bone dry. No cracks, no seepage, and so on. It drove me nuts.
I found the source one day when I went down into the basement one morning - water had accumulated in a window well, and once it got deep enough, it jetted across the room through the edge of the window for just a moment. The path of the stream dried out within an hour, while the area with the puddle stayed wet for a day. If I hadn't gone down to the basement at exactly the right moment, I'd probably have thought it was aliens, too. ;-)
- Rich