Debian on old or slow computer
Consider using LTS or OldStable instead of Stable. Some packages won't be supported in LTS. Links: LTS and CategoryLts.
Replace websites with special software
Use youtube-dl -f fmt (e.g. 36) to download videos from Youtube and other websites and play it with mplayer or vlc. The old version of the english Wikipedia article about YT has a list of YT formats (itags). youtube-dl is in the Backports. Another way to use youtube-dl is to download it to ~/bin and use youtube-dl -U to update it. See JensKorte/youtube-dl. If you get "WARNING: Your copy of avconv is outdated, update avconv to version 10-0 or newer if you encounter any errors." use the libav-tools from backports (as of writing: 6:10.1-1~bpo70+1). That version lacks ffplay which is used by winff to play files.
If your computer is too slow for iceweasel showing OpenStreetMap, try foxtrotgps.
xbmc or xbmc-standalone (xbmc with X but without a window manager) with radio, youtube or Mediathek plugin may or may not be useful for old computers (xbmc requires 24bit colors).
In the Debian repositories
claws-mail (former sylpheed) is a small mail programm with the look'n'feel of thunderbird/icedove. It features pop3, imap, smtp, spam-filter, encryption and plugins. clawsker is an extra utility for configuration.
dradio is a terminal based frontend for mplayer. It plays the preconfigured danish radio and TV channels. You can configure your own channels in ~/.config/dradio/menu.xml . The config file format is described in dradio(5).
pinta is a small, but powerful paint. It doesn't print pictures.
ripit rips audio cds with the help of lame or other encoders and uses the cddb for naming. Usage example: nice -n19 ionice -c3 ripit -o /home/myuser/music -v new -S standard --eject --nointeraction --loop 1 --ripopt "-z 3"
streamripper rips audio streams into files.
dvtm dwm epdfview gscan2pdf iceweasel with plugins irssi lftp mosh (ssh for slow or unstable connections) nmon pydf qalc rtorrent screen scrot w3m (with w3m-img )
Software that is not in the debian repos
jave is a program to draw ascii-art
JensKorte/notecase is a hierarchical note manager (aka. outliner)
JensKorte/radio-browser.sh, a little script to listen to radio streams
JensKorte/scrap, a rogue-like game
JensKorte/slsc, a spreadsheet calculator like sc
JensKorte/tornado-game, a clone of an old C64 game
If you can watch small videos only, recode videos with: nice -n19 ionice -c3 mencoder -oac lavc -ovc lavc -lavcopts acodec=mp2:vcodec=mpeg2video:abitrate=128:autoaspect -of mpeg -vf scale=360:-2 -o small.mpeg big-source.avi
Make use of ionice (package util-linux). The CFQ has to be the active io scheduler in kernel (for kernel versions <5.0). Example: nice -n19 ionice -c3 aptitude update
A draft for reporting bugs by mail can be found at reportbug-by-mail