Experiment. Backup before you try anything.
du -h --max-depth 1 /var
Refine your /etc/rsyslog.conf and /etc/logrotate.conf setups to minimize the size of your logs. You can delete logfiles that are not in use.
# apt-get autoremove
# apt-get autoclean
The largest directory generated by apt is usually /var/cache/apt
If you do not want man pages and docs you can delete files
in the following directories
You might also check out localepurge