Can a player on the receiving team of a kick-off call and make a "fair catch" of the ball if the kick is squibbed down the field (i.e., it has touched the ground first and remains in the field of play)?
This is tagged "collegiate", so I'll give the NCAA rule.
NCAA Rule 2, Section 8, Article 1. c.
c. A valid or invalid fair catch signal deprives the receiving team of the opportunity to advance the ball. The ball is declared dead at the spot of the catch or recovery. If the catch preceeds the signal, the ball is dead when the signal is first given.
Giving the signal means the ball can not be advanced for any reason. The ball is dead at the spot of the recovery.
In the NFL, you also could not advance the ball, but it would not be a fair catch.