How do I find a list of Homebrew's installable packages?

Recently I installed Brew. How can I retrieve a list of available brew packages to install?

For people who, like me, land here wanting to search the available packages but are not in front of a Mac with a working Homebrew install:

The Homebrew site now has full lists and a search option on Homebrew Formulae.

The full lists are on separate pages for:

• Formulas: https://formulae.brew.sh/formula/
• Casks: https://formulae.brew.sh/cask/