Default user-group owner for /var folder
/var/ is probably the most complicated ownership setup in the entire operating system. It's not all root-owned and doing that is about as harmful as letting your user own it all. Some things won't work if you leave it like that, namely the desktop.
If you want to see the array of users and owners you're dealing with, look at the following command on a working system:
sudo ls -lR /var | awk '/^[^/]/ {print $3 " " $4}' | sort -u
On my system, 59 distinct user/owner combinations in /var/. This is the point where I expect most people give up and reinstall. Let's be honest, if you haven't gone that far with your computer, there isn't going to be much lost from a nice install-over-the-top. It's almost certainly going to be quicker.
If you're still reading, you're completely mad but you're in good company. Let's start by owning everything to root:root.
sudo chown -R root: /var
And now we have to correct for the things that aren't and can't be root. I have written short command that shows me the files and directories that aren't owned by root:root.
In the output I have trimmed out some things that aren't going to be relevant to a lot of people (nginx, rabbitmq, schroot stuff, lxc, and a lot more). This is all specialist stuff. If you've borked those permissions, ask me for the output and I'll include it. I have also broken down some big directories that are owned by the same user/group all the way through with wildcards.
I'm including this output so you can see how things are supposed to be owned. You can manually chown things to approximately the right user/group. oli is my $USER.
$ sudo find /var/ -not \( -user 0 -group 0 \) -not -path "/var/lib/schroot/*" -not -path "/var/cache/*" -not -path "/var/tmp/*" -printf "%p,%u:%g\n" | grep -viE "(squeeze|rabbitmq|nginx|lxc|postfix)" | sort -u | column -t -c 80 -s ,
/var/backups/gshadow.bak root:shadow
/var/backups/shadow.bak root:shadow
/var/crash/* root:whoopsie
/var/lib/avahi-autoipd/6c:f0:49:54:0b:80 avahi-autoipd:avahi-autoipd
/var/lib/avahi-autoipd avahi-autoipd:avahi-autoipd
/var/lib/colord/* colord:colord
/var/lib/libuuid libuuid:libuuid
/var/lib/mlocate/mlocate.db root:mlocate
/var/lib/nfs/sm.bak statd:nogroup
/var/lib/nfs/sm statd:nogroup
/var/lib/nfs statd:nogroup
/var/lib/nfs/state statd:root
/var/lib/samba/usershares/films oli:oli
/var/lib/samba/usershares/incoming oli:oli
/var/lib/samba/usershares root:sambashare
/var/lib/samba/usershares/tv oli:oli
/var/lib/sudo/oli/0 root:oli
/var/lib/sudo/oli/10 root:oli
/var/lib/sudo/oli/11 root:oli
/var/lib/sudo/oli/12 root:oli
/var/lib/sudo/oli/13 root:oli
/var/lib/sudo/oli/14 root:oli
/var/lib/sudo/oli/1 root:oli
/var/lib/sudo/oli/2 root:oli
/var/lib/sudo/oli/3 root:oli
/var/lib/sudo/oli/4 root:oli
/var/lib/sudo/oli/5 root:oli
/var/lib/sudo/oli/6 root:oli
/var/lib/sudo/oli/7 root:oli
/var/lib/sudo/oli/8 root:oli
/var/lib/sudo/oli/9 root:oli
/var/lib/sudo/oli/console root:oli
/var/lib/sudo/oli root:oli
/var/lib/sudo/oli/tty1 root:oli
/var/lib/sudo/oli/tty2 root:oli
/var/lib/lightdm/* lightdm:lightdm
/var/local root:staff
/var/log/apport.log.1 root:adm
/var/log/apport.log.2.gz root:adm
/var/log/apport.log.3.gz root:adm
/var/log/apport.log.4.gz root:adm
/var/log/apport.log.5.gz root:adm
/var/log/apport.log.6.gz root:adm
/var/log/apport.log.7.gz root:adm
/var/log/apport.log root:adm
/var/log/apt/term.log.1.gz root:adm
/var/log/apt/term.log.2.gz root:adm
/var/log/apt/term.log.3.gz root:adm
/var/log/apt/term.log.4.gz root:adm
/var/log/apt/term.log.5.gz root:adm
/var/log/apt/term.log.6.gz root:adm
/var/log/apt/term.log.7.gz root:adm
/var/log/apt/term.log root:adm
/var/log/auth.log.1 syslog:adm
/var/log/auth.log.2.gz syslog:adm
/var/log/auth.log.3.gz syslog:adm
/var/log/auth.log.4.gz syslog:adm
/var/log/auth.log syslog:adm
/var/log/boot root:adm
/var/log/btmp.1 root:utmp
/var/log/btmp root:utmp
/var/log/cups/access_log.1.gz root:adm
/var/log/cups/access_log.2.gz root:adm
/var/log/cups/access_log.3.gz root:adm
/var/log/cups/access_log.4.gz root:adm
/var/log/cups/access_log.5.gz root:adm
/var/log/cups/access_log.6.gz root:adm
/var/log/cups/access_log.7.gz root:adm
/var/log/cups/access_log root:adm
/var/log/cups/error_log.1.gz root:adm
/var/log/cups/error_log.2.gz root:adm
/var/log/cups/error_log.3.gz root:adm
/var/log/cups/error_log.4.gz root:adm
/var/log/cups/error_log.5.gz root:adm
/var/log/cups/error_log.6.gz root:adm
/var/log/cups/error_log.7.gz root:adm
/var/log/cups/error_log root:adm
/var/log/cups/page_log.1.gz root:adm
/var/log/cups/page_log.2.gz root:adm
/var/log/cups/page_log.3.gz root:adm
/var/log/cups/page_log.4.gz root:adm
/var/log/cups/page_log.5.gz root:adm
/var/log/cups/page_log.6.gz root:adm
/var/log/cups/page_log.7.gz root:lpadmin
/var/log/cups/page_log root:adm
/var/log/cups root:lpadmin
/var/log/dist-upgrade/20121107-0129/apt-term.log root:adm
/var/log/dist-upgrade/20130426-1402/apt-term.log root:adm
/var/log/dist-upgrade/apt-term.log root:adm
/var/log/dmesg.0 root:adm
/var/log/dmesg.1.gz root:adm
/var/log/dmesg.2.gz root:adm
/var/log/dmesg.3.gz root:adm
/var/log/dmesg.4.gz root:adm
/var/log/dmesg root:adm
/var/log/fail2ban.log.1 root:adm
/var/log/fail2ban.log.2.gz root:adm
/var/log/fail2ban.log.3.gz root:adm
/var/log/fail2ban.log.4.gz root:adm
/var/log/fail2ban.log root:adm
/var/log/fsck/checkfs root:adm
/var/log/fsck/checkroot root:adm
/var/log/hp/hp-upgrade.log oli:oli
/var/log/hp root:lp
/var/log/hp/tmp root:lp
/var/log/installer/syslog syslog:adm
/var/log/kern.log.1 syslog:adm
/var/log/kern.log.2.gz syslog:adm
/var/log/kern.log.3.gz syslog:adm
/var/log/kern.log.4.gz syslog:adm
/var/log/kern.log syslog:adm
/var/log/lastlog root:utmp
/var/log/mail.err.1 syslog:adm
/var/log/mail.err.2.gz syslog:adm
/var/log/mail.err.3.gz syslog:adm
/var/log/mail.err.4.gz syslog:adm
/var/log/mail.err syslog:adm
/var/log/mail.log.1 syslog:adm
/var/log/mail.log.2.gz syslog:adm
/var/log/mail.log.3.gz syslog:adm
/var/log/mail.log.4.gz syslog:adm
/var/log/mail.log syslog:adm
/var/log/news/news.crit syslog:adm
/var/log/news/news.err syslog:adm
/var/log/news/news.notice syslog:adm
/var/log/speech-dispatcher speech-dispatcher:root
/var/log/syslog.1 syslog:adm
/var/log/syslog.2.gz syslog:adm
/var/log/syslog.3.gz syslog:adm
/var/log/syslog.4.gz syslog:adm
/var/log/syslog.5.gz syslog:adm
/var/log/syslog.6.gz syslog:adm
/var/log/syslog.7.gz syslog:adm
/var/log/syslog syslog:adm
/var/log/ufw.log.1 syslog:adm
/var/log/ufw.log syslog:adm
/var/log/wtmp.1 root:utmp
/var/log/wtmp root:utmp
/var/mail/oli oli:mail
/var/mail root:mail
/var/mail/root root:mail
/var/metrics root:whoopsie
/var/spool/cron/atjobs/a000020152342b oli:daemon
/var/spool/cron/atjobs daemon:daemon
/var/spool/cron/atjobs/.SEQ daemon:daemon
/var/spool/cron/atspool daemon:daemon
/var/spool/cron/crontabs/oli oli:crontab
/var/spool/cron/crontabs root:crontab
/var/spool/cups/c00075 root:lp
/var/spool/cups/c00076 root:lp
/var/spool/cups/c00077 root:lp
/var/spool/cups/c00078 root:lp
/var/spool/cups/d00075-001 root:lp
/var/spool/cups/d00076-001 root:lp
/var/spool/cups/d00077-001 root:lp
/var/spool/cups/d00078-001 root:lp
/var/spool/cups root:lp
/var/spool/cups/tmp root:lp
/var/spool/rsyslog syslog:adm