Is there some application for selecting a file in Windows Explorer, and copy its file path to the clipboard, with one shortcut?
Does Windows have some built-in tool for it?
It's built in to Windows...
Shift + Right-Click the file -> Copy As Path
More Info: Get the Full Path of a Folder or File in Windows 7
Additionally here's a page that explains how to add custom entries to show on the non-Shifted context menu:
Copy File Path And Name Using Windows Explorer Context Menu Extensions
Yes. If you're using Windows' built-in explorer (not Internet Explorer), you can hold down the SHIFT key and press right click on the item (which can be a file or folder). Then the only thing you need to do is select the "Copy as path" option. Now the path of the item will be placed in your clipboard and you can use it by pasting it anywhere.
I use Path Copy Copy for that which supports various paths including UNC, Internet style, Unix, Cygwin and so on. Its context menu is fully configurable so you can leave your favourites there. "Long Path" and "UNC Path" are my favourites.
For the moment I've found Copy path for Windows that:
that will allow you to right click on a drive or file system object and copy the path of the file to the clipbpoard. If the drive is a mapped drive or the file system object exits on a mapped drive it will resolve the full UNC path..