Well, well, well, Steam really corrupted things this time. This week they added a survey that detected the software installed on a user’s system, and I can only guess that their changes caused the trouble. I could not connect to the Steam server for several days in a row, and I did not see any new posts from other users with the same problem. Thus the problem had to be on my system.
From an old newsgroup I found this handy tidbit: Rename the file ClientRegistry.blob.
I did as told, and Steam then updated itself, and connected successfully.
Here is a reference article on Steam’s web site: