These are 2player games requiring only a pile of counters or some other conveniently sized objects (buttons, coins, matchsticks, stones, paperclips, sweets etc.) 
Nim 
This is the best known of this type of game and has many variations. The form in which it most often appears is as follows. Arrange 15 counters into 3 groups of 3, 5 and 7. Players take turns at taking out counters from these groups. A player may take as many counters (but at least one) as he or she chooses, but all the counters taken must be from the same group. The winner is the player who takes the last counter (or counters). 
Bachet's Game 
Put several counters down to make a single group. Though almost any size of group can be used, between 15 and 25 counters make for a reasonable game. In their turns, players take 1, 2 or 3 counters from the group. The winner is the player who takes the last counter (or counters).

Tsyanshidzi 
Put several counters down to form two groups of different sizes (say a 13 and a 17).
Each player in turn may make one of the following moves 

1.  Take any number of counters from one group.   OR  2.  Take the same number of counters from both groups. 

The winner is the player who takes the last counter (or counters). 
Skittles 
Arrange several counters in a straight line with each one touching (or assumed to be touching) those either side. In their turns, players may take out 1 or 2 counters from anywhere in the line, but 2 may only be taken provided they are 'touching' each other. The winner is the player who takes the last counter (or counters).

Lasker's Nim 
Arrange 15 counters into 3 groups of 3, 5 and 7. Each player in turn may make one of the following moves 

1.  Take any number of counters from one group.   OR  2.  Divide any one group into two groups. 

The winner is the player who takes the last counter (or counters). 
Grundy's Game 
Arrange several counters into groups.
There can be any number of groups (from 1 upwards) and any number of counters (greater than 3) in each group, but 3 groups with between 9 and 13 counters in each group make a reasonable starting position.
Each player in turn has to divide any one group into 2 groups of different sizes (so a group of 1 or 2 counters cannot be divided).
The winner is the last player who is able to make an allowed move. 