What position takes the most moves to solve for the jail puzzle (Klotski)?
As the wikipedia article states, there are many, many names for that puzzle. 
 I'm a bit surprised, the Wikipedia article does not mention an exhaustive analysis documented in the book Winning Ways for your Mathematical Plays, Vol 2.  The authors state that the longest possible puzzle has the starting position:

1441
2442
2022
1021
5566


and the ending position is the flipped version of that position.  They call it the "Century and a half" puzzle, and state it's the longest sliding block puzzle with those pieces.  They also provide a "map" that shows the entire space of configurations, and how to move between them.