This really depends on how you want to further develop the program. If it's always going to be a single countdown timer, then it really doesn't matter. I'd toss it in the registry, just to avoid pointless file clutter.

If you intend to run multiple instances of the program, each counting down a different option, then I'd make an .ini/.dat file, and provide a commandline option to pick which file to use for each instance of the application.

If you want to make this thing seriously useful, I'd build in support for multiple countdowns, alarms, icons, etc into the program itself. Then I'd also store everything in the registry again, because that's where that sort of stuff really should go, and the program's interface would allow for altering the registry accordingly.

The only real reason to use a .ini file is that it makes porting to older Windows environments easier (but who uses 3.0 any more?), and it makes backing up the configuration easier. I don't think people will care if they loose their counter settings when they reinstall Windows.

make it a delphi clx application
then use ini or something
that way you can port it to linux if need be