I tried resetting the App Store and cleaning cookies, as well as doing the Spotlight Re-index and nothing helped. Someone on another forum suggested resetting the PRAM but that didn't help either. Another suggested clearing Safari's history and web site data and that, too, didn't help.
Another said it may be caused if you have an external drive with a backup of your system on it. If that external drive is indexed by Spotlight, then the App store will see the old version in the backup and want to update it. But App store updates the version on the internal drive, so the backup never gets touched (wouldn't want it to, anyway, as it is a backup), so App Store keeps suggesting updates.
I then tried restarting in Safe Mode to see if the updates appeared, and they did. When I restarted in normal mode, the updates no longer appeared. Hopefully for good, but time will tell. If it reappears, I may try reinstalling Yosemite again. So, I'm really not sure what corrected the problem, but it's gone - for now.