I am looking for an application I can install in Windows XP to share one of it's directories over Internet with password protection. Ideally I could install it on clients machines so they can use it like regular windows directory. I can't use Dropbox or similar clouds tools because of their license. Is there such application?
You can try to setup an FTP server (assuming your machine is online at the time people need to access the files). It's password protected and once the clients log in, they will see it like a regular directory with optionally write access.
Start > Control Panel > "Add/Remove Windows Components." > "Windows Components." > "Internet Information Services" > "details" > enable "File Transfer Protocol (FTP)" service.
Follow the instructions for the install Wizard. It may request you to insert your Windows XP CD. The shared directory is "C:\INETPUB\FTPROOT" by default.