Just reporting back as I started this thread.
A quick recap, I used Hal's scripts to identify the huge files (spotlight + plus another oddly large file or two). I then used his hints to remove the large files (including multiple restarts, multiple uses of DU, etc), but the files again quickly grew. It also seemed that the background process that was creating the files was using much of the processing power, thus slowing the computer.
I then did a clean install, followed by use of Migration Assistant to bring back files, apps, etc. Alas, the behavior resurfaced.
Exasperated, I did another erase and install, but this time I reinstalled each app. Used .Mac to bring back Mail settings, address books, bookmarks etc. and my iDisk to get back my main documents. Other documents, I retrieved from my backup. This was, of course, considerable work as I had to find old install disks, re-download apps, dig out and re-enter all the registration codes, apply all new updates, etc (I have had problems in getting Microsoft Office to apply all its updates). That also meant, I had to reset all my preferences -- one at a time. Luckily, this MacBook is not my main computer and I've not loaded it up as much as my other two.
The long and short of it is, though, that the problem has not happened again. I was traveling yesterday and used the MacBook for much of the day -- including jumping onto several different Wi-Fi networks. I haven't seen any sign of the old problem.
So, while I don't know what it was (and don't have the time to try to find it), I'd have to guess that something that doesn't work with Leopard was being brought forward. The completely clean install with clean install of all apps and resetting of preferences seems to have worked.
Let me add one more thing, I have upgraded two other computers with archive and install, one a G5 iMac and the other a late model Intel iMac. I haven't experienced this or any other problem on either of them and both of them have many more apps & other files.
Go figure!