I'd like to use a tiling window manager like xmonad. However, I want my windows to have titles. How can I configure xmonad in such a way that my windows always have titles?
XMonad.Layout.NoFrillsDecoration module from xmonad-contrib will do what you want, see the documentation for how to set this up in your config file.
The titles never go away, they just don't show unless you make them show somewhere. I would strongly recommend that you use something like xmobar to get your titles back. It is what I use.
XMobar is the very top bar in this screenshot: