To finally get away from services like ICQ or Skype I run my own XMPP server from now – this means my e-mail-address is also my contact address (see “About me”) for XMPP (formerly also known as “Jabber”).
At the moment I am experimenting with Jitsi, but there are also a number of mobile clients which support XMPP/Jabber as well.
Update 2020-07-05
I don’t use Jabber any longer but Signal instead. Jitsi ist now known for the free video conference solution “Jitsi Meet” which I’ve been using on my server for a while.