One exceedingly powerful and often overlooked ability of syslog is to log messages to a remote host running syslog. This allows you to cryptographically sign logs to ensure they haven't been tampered with. Nsyslogd Nsyslogd supports tcp, and SSL for logging to remote systems. There are a variety of tools to automate these tasks however. WOTS collects log files from multiple sources and will generate reports or take action based on what you tell it to do.
Kernel logging The lowest level of logging possible is at the kernel level.
Shell logging A variety of command shells have built in logging capabilities. Everything from the command prompt style to how many lines to keep in the log file. Doing this however opens up some legal issues, so make sure your users are aware they are being logged and have agreed to it, otherwise you could get into trouble.