Some of my favourite free, modern-looking, easy to use, web-based email clients that anyone can install and use with their mail server (in no particular order).

Roundcube
Website – Screenshots

  • Built-in calendar, contacts and task list
  • VERY advanced filters
  • PGP support
  • Multiple identities/e-mail accounts
  • Many – too many – skins (free and paid)
  • A few responsive skins (default isn’t)

RainLoop
Website – Screenshots – Demo

  • Single-pane or horizontal/vertical split
  • Advanced filtering (using Sieve)
  • Two-factor authentication
  • OpenPGP support (client-side JS)
  • No mobile support

MailPile
Website – Demo

  • Tag-based sorting
  • OpenPGP support
  • Multiple identities/e-mail accounts
  • No mobile support
  • Not (yet) multi-user

AfterLogin WebMail Lite
Website – Demo

  • Contact manager with groups
  • Multiple identities/e-mail accounts
  • No mobile support

Neutron (ProtonMail WebClient)
GitHub – Screenshots

  • A server for the ProtonMail WebClient
  • OpenPGP support
  • Fully responsive