This password should have been recorded in my Keychain. Unfortunately, it wasn't (possibly because I installed Tiger as a Jaguar update). No matter. If the password wasn't in the Keychain, it was elsewhere! SO I looked in a lot of places, and tried tons of tricks, to find my password.
There are always things you never think of and places you never visit. Looking for something else, I opened System Profiler. I was browsing the window when I noticed the Network branch and the Configuration entry within it. I clicked on it, and all my configurations were there. When I clicked on my modem connection entry, I saw a magic word: password, followed by hex numbers.
After a short hex decode (each four hex digits match one character), my password was mine again. I was pleased. Now I do consider this a security concern, but I'm glad it was there.
[robg adds: I can't confirm this one, as I don't have a configured modem...]

