Firstly, you must find out what is eating away at your space. I'd suggest you track down the physical file or directory that grows to that size.
The simplest way would be to check the directories in / using: ( I'd suggest running it as root )
# du -hs /* 2> /dev/null 4.2M /bin 25M /boot 204K /dev 6.7M /etc 19G /home 112M /lib 16K /lost+found 12K /media 16K /mnt 4.0K /multimedia 1018M /opt 0 /proc 15M /root 8.6M /sbin 12K /srv 4.2M /storage 0 /sys 108K /tmp 16G /usr 4.3G /var
Now, You run that when the computer has freshly started and has not started to eat space yet and you save the output in a file ( ~/record-space )
$ sudo du -hs /* 2> /dev/null 1> ~/record-space
And then when your computer is nearing a "FULL" state, you can run the command again saving the output in a second file.
$ sudo du -hs /* 2> /dev/null 1> ~/record-space2
Now you can compare these two files ( ~/record-space and ~/record-space2 ) to see how th e main directories differ...
My favourite way of comparing files is using diff:
$ diff ~/record-space{,2}
update: See Gille's comment to this answer.
Instead of du -hs /*, rather use du -xsh /tmp/* /var/*/* ~/.*.
/tmp)/var/logs?/tmp; in particular, if you delete/tmp/.X11-unix/X0, you won't be able to start GUI programs. If you see a large file there, try to work out who is using it, don't delete it if you're not sure you can do it safely.