Debian on old or slow computer
Consider using LTS or OldStable instead of Stable. Debian 6.0 (squeeze) will get a special Long-Term-Support (LTS) for i386 and amd64 until February 2016. Some packages won't be supported like libwebkit* and its browsers. Add Backports to your repos to get more software. 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 english Wikipedia article about YT has a list of YT formats. 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. A disadvantage is the lacking manpage, but youtube-dl -h gives you help.
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.
Software that is not in the debian repos
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. Example: nice -n19 ionice -c3 aptitude update