tmux and screen-256 TERM not supported on remote hosts

You can copy the necessary terminfo descriptions to remote hosts.

1. On the local system, dump the description to text format:

   infocmp xterm-256color > xterm-256color.ti
   infocmp screen-256color > screen-256color.ti
   

2. Copy to the remote host and compile:

   tic xterm-256color.ti
   tic screen-256color.ti
   

The descriptions will be stored in ~/.terminfo.

(infocmp and tic are part of the ncurses or ncurses-bin packages in most Linux distributions, as well as most BSDs that use ncurses.)

I have this in my .bashrc:

alias ssh='TERM=screen ssh'