A boy is walking down the street to get to his friends house, he
doesn't have much time.  He approaches the corner and he can make a
left or a right.  There is a boy standing on the corner (knowing that
50% of people are good and 50% are bad - (meaning the boy can lie),
what is one question he can ask the boy to find out which way to go?

Hi mbroom and thanks for the question!

I will assume that if a person is bad then he or she always lies and
if a person is good then he or she always tells the truth. 
Furthermore, I will assume that the boy standing at the corner knows
the correct direction.

The traveler should ask the boy on the corner the following question:

Question: "If I were to ask you if going to the left is the correct
direction, would you answer 'yes'?"

Let us first consider the case in which the boy on the corner is a
liar:

If the left is the correct direction, then the boy will answer 'yes'
since answering 'yes' would be a lie: if the traveler were to ask him
if going to the left is the correct direction he would *not* say
'yes'.

If the left is the incorrect direction, then the boy will answer 'no'
since answering 'no' would be a lie: if the traveler were to ask him
if going to the left is the correct direction he would say  'yes'.

Now let us consider the case in which the boy on the corner tells the
truth:

If the left is the correct direction, then the boy will answer 'yes'
since answering 'yes' would be the truth: if the traveler were to ask
him if going to the left is the correct direction, he would say 'yes'

If the left is the incorrect direction, then the boy will answer 'no'
since answering 'no' would be the truth: if the traveler were to ask
him if going to the left is the correct direction, he would *not* say
'yes'

OK, so the interesting result is that whether the boy is a liar or a
truthteller, the answer he gives to the question will be the same.  If
he answers 'yes' then the traveler should go to the left.  If he
answers 'no' then the traveler should go to the right.

Additional links:

This puzzle is a version of a puzzle given by Raymond Smullyan.  More
such puzzles may be found in his book entitled: What is the Name of
this Book? which can be found at:
http://www.amazon.com/exec/obidos/tg/detail/-/0139550887/qid=1064327727/sr=1-13/ref=sr_1_13/104-1019769-4771157?v=glance&s=books

More info on Smullyan can be found at:
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Smullyan.html

Search strategy:
smullyan 
smullyan fork

If you are unsatisfied with any portion of this answer please request
clarification prior to submitting a rating.

Best of luck!

-blinkwilliams-ga

Blinkwilliams answer was not only thorough it was quick as well!

Thanks, Blinkwilliams!

A more straightforward question is:
"If I were to ask you which way to go, what would your answer be?"

Following the same logic as above, the boy would then have to give you
the correct directions.

alex_p