Nearly every time I launch Bryce it makes me enter my name and serial number. It seems to accept my serial number, but it doesn't seem to keep it. Any ideas?
You didn't say which operating system you use, but assuming you have Windows 7, it is probably a UAC problem.
Win 7 doesn't like anything writing to "Program Files" folders. You should probably reinstall to a location outside of "Program.Files".
Modern programs usually make a writeable section in "User/documents..." or the like to overcome this.