My most common uses are for going through config files, error reports and logs.
dmesg | grep (hardware device)
usefull for finding hardware errors in your kernel
cat /var/log/Xorg.cong | grep EE
Useful for finding errors in your xorg.conf file. Try it with WW to find the warnings to iron them out if your a perfectionist. Or it might be /var/log/XFree86.0.log if you're slow on the update tip.
The -A and -B flags are useful for specifiy how many lines you want to display after and before the occurence of the pattern.
I'm sure there are plenty more very useful functions for this amazing utility. Grep has been around since the begining of unix for good reason. It is even on this system from 1970 I'm working on right now.