Each log serves it's own purpose. It really depends on what you're trying to check for. Some common ones are outlined below:
/var/log/auth.log - Information pertaining to authentication - including sudo/su activity
/var/log/boot.log - All information during the booting process
/var/log/crond.log - Information from cron daemon
/var/log/messages - Typical dumping point for messages not regarding the system
/var/log/pm-suspend.log - Logged during the Power management suspend function
/var/log/user.log - Information from all userlevels
/var/log/syslog - This organizes output from different softwares and is a "general log"
/var/log/kern.log - Information being logged from the kernel
There are additional logs - like the apache2 folder, mysql.log/mysql.err, and others. These are all software specific - if you don't have apache2 installed, you won't have the log files for it. The only time you would want to check logs is when an issue arises - most of the time though it'll be okay to let them sit in the dark.