What is palindromic DNA? What is palindromic DNA and why isn't every complementary strand palindromic?

I know AGCT is palindromic, but what is an example of a strand that isn't?
A palindromic stretch of DNA is a strand whose reverse complement is itself.  So 5'-AAAT-3' is not palindromic.  It's reverse complement is 5'-ATTT-3'.  Those two pieces of DNA are not identical.  However, 5'-GGATCC-3' is palindromic, because the reverse complement is identical.