This does not sound like typical behavior for a FileMaker file, but in current versions such as version 11, there are two places that control security settings for your computer: Manage | security--where accounts and passwords are created and File Options--where you can specify what account name and password--if any is automatically used to open the file.
If you have not made any changes in Manage | Security, then likely a change occurred in File Options. The default setting for a FileMaker file is to auto enter Admin as the account name and no password. This allows the file to open without asking for a password as long as the admin account is not modified to specify a password.
The other issue that can trip up users on files that have accounts and passwords defined is that passwords are case sensitive. If you enter OpenSesame as the password for an account in Manage | Security, opensesame will not allow you to open the file.
Thanks for a very clear response that gave me a solution.
Since I had never made changes in Manage I Security (i just upgraded from Filemaker 2, 3,4, etc. and then one day I had this difficulty), here's what I did. When the window came up presenting the account name (basically the name of my computer) and also had that password prompt to fill in. I changed the account name to "Admin" and entered no password. The database I had most recently created opened immediately.
I will go back to older databases that I could no longer get into, and do the same procedure: make sure the account name is "Admin" and no password.
Once you have the file open, you can go to File Options and specify admin and no password there and the file will stop asking you for a password when you open the file.
Oh yes, and filemaker enters the USER NAME as the default ACCOUNT NAME when it pops up the password dialog. User names are specified in preferences and can be different with each user account on your computer.