I wonder what Vim Taglist is good for if I cannot jump to a tags definition from within an open source file. Do I have to generate a separate tags file by running, say, ctags *.f90, in order to be able to use Ctrl+]?
Yes, you need a tags database (usually created by running ctags or an equivalent external tool) to use the tag jump / search functionality of Vim.
As Vim is a general-purpose text editor, it does not possess any knowledge about individual languages, and instead delegates (in true spirit of Unix's do one thing well mantra) this to an external resource.
PS: There are plugins like easytags.vim that automate the process of tags generation and update.