I've seen them used to create inline infinite lists:
(loop for loop-this in '#1=(:a :b :c . #1#)
for just-once in '(1 2 3 4 5 6 7)
do (format t "~S => ~S~%" just-once loop-this))
=>
1 => :A
2 => :B
3 => :C
4 => :A
5 => :B
6 => :C
7 => :A
NIL
This encapsulates the "loop over this list forever" at its definition, instead of making me use an array and using length/modulo where it's used. There are of course many other solutions, but this one is both short and perfectly describes what I want.
Many Lisp library functions take lists as inputs (no kidding!), so this is a very efficient alternative to actually creating a repetitive list. (Pythoners: think itertools.cycle).
Also, any time you want to build a simple-but-not-trivial graph inline (great for unit testing), these come in handy.
