As of late May, 2021, Sublime Text 4 has been released. As a result, the old solution to installing Sublime Text 3 via Homebrew will now install Sublime Text 4 instead. If this is what you actually want, then the following brew installation command will install it:
brew install --cask sublime-text
Currently, there is no available cask on Homebrew which will allow the installation of Sublime Text 3 instead of Sublime Text 4.
As a side note, Sublime Text 2 is available in the sublime-text2 cask.
Historical note: This question originally was motivated by the fact that the sublime-text cask was Sublime Text 2 instead of Sublime Text 3. As of around May 2016, this is no longer the case.
Turns out now brew cask install sublime-text installs the most up to date version (e.g. 3) by default and brew cask is now part of the standard brew-installation.