Take three pennies and three nickels and arrange them in a row, alternating penny and nickel. The goal is to move them so that the coins are again in a row, with all pennies to the right of all the nickels. Each move consists in placing your index and middle finger on a pair of adjacent coins, and sliding those two coins to a new position (without rotating!). This can be done in three moves. 
Starting Position
Goal 
Take nine pennies and arrange them in a 3 by 3 grid.
There are now eight straight lines that each pass
through three pennies: three horizontal, three vertical
and two diagonal.
Your goal is to move exactly two pennies so that there
are ten straight lines, each with three pennies.
In the solution, there are no straight lines with more than three pennies, and no penny is placed on top of another. 
Take eight pennies and arrange them in row.
Your goal is end up with four piles of two pennies each.
Each move consists of picking up a penny, jumping in
either direction over two "piles" and landing on the
third. Each pile may consist of a single coin or two coins.
This must be done in four moves.
It is not necessary that the final four piles be adjacent! 
Starting Position

Starting Position

Take five pennies and five quarters, and arrange them alternating in a circle. Your goal is produce five piles, each with a penny on top of a quarter. Each move consists of picking up a penny, moving in either direction around the circle, jumping over two "piles", and landing on the third. Each pile can be one or two coins. This must be done in five moves. 
Take six pennies and arrange them in a triangle. Your goal is to rearrange the pennies into a hexagon in four moves. Each move consists of sliding a single penny to a new location. The new location must be touching at least two other pennies at each step. 
Starting Position

Goal 
Here we have nine pennies arranged in a triangle. Can you slide exactly two pennies to form a square? 
Take three quarters and two pennies and arrange them in a row,
in alternating order.
Your goal is to rearrange them so that the quarters are all to the left
of the pennies.
On each move, you place your index and middle finger on two coins, and move them to another location on the line. You may not switch the order during a move. Furthermore, you must move one penny and one quarter with each move. You're not allowed to move two pennies or two quarters in a move. The goal can be reached in four moves. Good luck! Note: the final configuration does not have to be at the same location along the line. 
Starting Position

Starting Position

Take two quarters, two pennies and two dimes, and lay them out in a row,
in the order quarter, penny, dime, quarter, penny, dime.
Your goal is to rearrange these coins so that each pair of like coins
is adjacent (e.g. quarter, quarter, penny, penny, dime, dime).
Each move consists of placing your index and middle fingers on a pair
of adjacent coins, and sliding the pair to another location in the row.
The two coins being moved must be different, and you are not permitted to change the order of the coins during the slide. You are allowed three moves. For bonus points, find a solution where the coins end up in the same six positions where they started! 
This is a game for two players.
Start by drawing a row of squares.
The number of squares is not importnat,
but ten to fifteen is a reasonable number.
Next, place coins in some of the squares. Four or five coins makes for an interesting game. For simplicity, we use just three coins in the example.
The players decide who goes first, and them take turns moving. Each move consists in sliding a single coin one or more squares from left to right. The moving coin cannot land on, or jump over, another coin. The last player to move is the winner. Here is a sample game: 

Start:  
A:  
B:  
A:  
This is a bad move for A, since it lets B force a win with this move:  
B:  
A:  
A can only move the middle coin. Even if he slides by just one square, B follows behind him with the last coin.  
B:  
And B wins since A has no more moves! 