A strange loop is a case of self-reference which affects (or even damages) the original item, possibly causing a paradox. I love this example:
A sketch on Late Night with Conan O’Brien once had Conan (seemingly spontaneously) become upset with a cue-card holder and tell him to leave the set; immediately, the cue-card holder was shown, holding a card with Conan’s “you’d better leave” line written on it.
Another example of sorts is that great Hofstadter quote: “This sentence contradicts itself – no actually it doesn’t.” What does this mean about me? I’ll leave that to you to decide.