2D Grid Games such as snakes and ladders, ludo, monopoly, cribbage, checkers, chess
Related Games Mahjong, dominos, memory(concentration) which are 2D but not on a 
fixed "board"
There are many commercial and amateur "grid games" and a tool kit for building these is 
good first step.

Simplest grid games take a one-dimensional path (set of squares) and map them onto 2D 
board with possible nifty graphics such as a snake that links one square to another
16 15 14 13
12 11 10   9  This is an example of a path 16 squares long
8    7   6   5    on a 4 by 4 board
4    3   2   1

N players who start at same time at position 0 and take turns. N>=2
Typically you "roll a dice" (choose a random number R usually from 1 to 6 but 
sometimes 1 to 12 for 2 dice) and player moves R places landing on a new square. 
Squares are associated with actions (such as "miss a turn", "move up a ladder to a later 
square" etc.) Sophisticated games are associated with money and money changes 
between players and bank as one of actions on a square.
"Winning" in simplest games is reaching the last square -- one can enforce if you want 
requirement of exactly correct last move e.g. if you are at square 14 and need to get to 16. 
Then one ignores moves with R>2 and win with R=2 or two R=1 moves.