Tony is taller than Sam. Harry is not taller than Tony. Danny is taller than Tony. Sam is shorter than John. At least one person is shorter than Sam and at least two people are taller than John. Who is the tallest person?

In terms of height, Tony > Sam.
Tony $$\ge\ $$Harry
Danny>Tony
John>Sam
At least one person is shorter than Sam, and at least two people are taller than John. 

In order to find the tallest person, we can easily see that John cannot be the tallest (he has at least two people taller than him), Sam is shorter than Tony, Danny is taller than Tony and Harry. making everyone have someone taller than them except Danny. 
Therefore, Danny would be the tallest of all of these.