syslog-notify, a utilty for modern Linux (and other Unix-like) desktops, provides a convenient pop-up display for messages that would otherwise be written unnoticed to the system logs. The choice of messages to display (from all messages to only the most critical) is completely configurable through the standard syslog configuration files. Popups are handled via the freedesktop.org notification standard, and thus is fully integrated with the desktop environment, e.g. Ubuntu's NotifyOSD or the standard Gnome notification-daemon that ships with many distributions.
In short: if you want to be informed about what your computer is doing, syslog-notify is for you.