I mean the famous example is of course,
(define (eval exp env)
(cond ((number? exp) exp)
((string? exp) exp)
((symbol? exp) (lookup exp env)
((eq? (car exp) 'quote) (cadr exp))
((eq? (car exp) 'lambda)
(list 'closure (cdr exp) env))
((eq? (car exp) 'cond) (eval-cond (cdr exp))
(else (apply
(eval (car exp) env)
(eval-list (cdr exp) env)))))
which uses a Lisp to define itself. This means roughly that if you understand enough Lisp to understand this program (and the little recursive offshoots like eval-cond), there is nothing else that you have to learn about Lisp. You officially have read the whole language reference and it is all down to libraries after that. Compare e.g. with trying to write Rust in Rust where I don't think it could be such a short program, so it takes years to feel like you fully understand Rust.
Indirectly this also means that lisps are very close at hand for “I want to add a scripting language onto this thing but I don't want to, say, embed the whole Lua interpreter” and it allows you to store user programs in a JSON column, say. You also can adapt this to serialize environments so that you can send a read-only lexical closure from computer to computer, plenty of situations like that.
Aside from the most famous, you have things like this:
1. The heart of logic programming is also only about 50 lines of Scheme if you want to read that:
https://github.com/jasonhemann/microKanren/blob/master/micro...
2. Hygienic macros in Rust probably owe their existence to their appearance in Lisps.
C2 asks the same question here: https://wiki.c2.com/?LispShowOffExamples with answers like
3. The object model available in Common Lisp was more powerful than languages like Java/C++ because it had to fit into Lisp terms (“the art of the metaobject protocol” was the 1991 book that explained the more powerful substructure lurking underneath this object system), so a CL programmer could maybe use it to write a quick sort of aspect-oriented programming that would match your needs.
4. Over there a link shows how in 16 LOC you can implement a new domain-specific language to define and run finite state machines: http://www.findinglisp.com/blog/2004/06/automaton-cleanup.ht...