Interesting thought:

If someone were to say "I am a liar", it would be self defeating, because you would be required to trust them enough to believe them, in which case, they wouldn't be a liar. And if a person who tells the truth says that he is a liar, then he's really lying in which case he isn't really telling the truth.

If someone were to say "I always tell the truth" it would be really hard to discern if he was a liar or a truthful person. The liar would of course lie and says he tells the truth, and the truthsayer would just be stating fact.

So, therefore, you could never ask a person if they are a liar or not. You could never get a straight answer from the liar, and based on that, you could never figure out who isn't a liar.