log files of note on Linux

/var/log/syslog or /var/log/messages Shows general messages and info regarding the system. Basically a data log of all activity throughout the global system.

/var/log/auth.log or /var/log/secure Keep authentication logs for both successful or failed logins, and authentication processes.

/var/log/cron.log keeps a record of Crond-related messages (cron jobs). Like when the cron daemon started a job.

/var/log/mail.log is for mail server logs, handy for postfix, smtpd, or email-related services info running on your server.

/var/log/boot.log start-up messages and boot info.

/var/log/kern keeps in Kernel logs and warning info. Also useful to fix problems with custom kernels.

/var/log/dmesg a repository for device driver messages. Use dmesg to see messages in this file.

/var/log/daemon.log keeps track of running background services but doesn’t represent them graphically.