Well, this is a challenge for me, but you can try another similar one!
If you visit Hans webpages, you already have noticed the Hans37, Hans38 and Hans39 contests! Each year, like everybody, Hans have an one year increase to his age. We, to celebrate his great work, invent some new games where the board must have the number of squares exactly equal to his age at that moment. My point here, is that we only started at 37, and his past? Nobody remembers his past? I did! Or at least I'm trying! :)
Well, not all are chess games, but almost all are playable and I try to use nothing more than the usual equipment.Some games can turn out to be fun for kids that are giving their 1st steps with games and puzzles, some others can be challenging to many of us.
Another thing:
There are thousands of games out there. I wanted to be as original as possible, but that does not mean that every game is a new one. Sometimes I took ideas from other games, like Tetris or Set. Possibly, there are very close variations about already existing games. If that happens, I’m sorry, that was not my intention.
On the other side, I would enjoy very much if someone pick one or more of these games, twist them and create better games using the original concept. Feel free to do that!
Introductory Notes:
Piece : King(K), Queen(Q), Rook(R), Bishop(B) or Knight(N)  
Unit : Piece or Pawn(P) 
All games are for only two players: white (W) and black (B)!  
By default, all units behave like in FIDE chess.  
In board diagrams, I use ‘O’ to represent white pawns. 
Hans1 : Putting the piece!
Board
++
 
++
Rules
Sample Game
White: Joao Neto (with knight)
Black: Carl Lewis (with queen)
01
Remarks
Try to win a Hans1 game against carl lewis with an horse on your back! 
Hans2 : Hey, that square is mine!
Board
+++
  
+++
a b
Rules
Each player have a set of 1 King, 1 Queen, 2 Rooks, 2 Bishops and 2 Knights. 
Piece values: K=8, Q=7, R=5, B=4, N=3. 
Notation
x?y = pick piece x and try to put it on square y  
x!y = piece at square x supports piece at square y  
x^y = piece x jumps to square y 
Sample Game
Moves (W vs B) Result so far:
1. N?a B?a 03
(the W knight is taken, now there is
a B bishop at square a)
2. B^b Q?a 03 (the
bishop escaped by an inch!)
3. B!a,R?a Q!a 03 (there is a tie! Q!a
values 9 points,
B+R = 4+5 = 9. So all disappear)
4. B?b N?a 03
5. B!b,R?a N!a,R?b 010 (at square a, the selfsupported
knight values 5 against the rook=5,
so both disappear. The selfsupported
bishop values 6 against the W rook=5,
so the W rook is taken, 5 points for B
plus one more point because the bishop
stand on the same square)
...
Remarks
This game can be easily transformed to work in a board of n squares. 
Hans3 : Meeting in Battle Field a2
Board
+++
   2
+++
  1
++
a b
Rules
Each player have a set of 1 King, 1 Queen, 2 Rooks, 2 Bishops and 2 Knights.  
Piece values: K=8, Q=7, R=5, B=4, N=3. 
Sample Game (^  means piece taken)
White: Q B N B R R N K
^
^ ^
Black: B B R R N N Q K
^
^ ^ ^
Result: 1218
Remarks
I know that I just need one square for this game, but I prefer the actual Hans1 as an introduction! ;) 
Hans4 : Don’t clean the Board!
Board
+++
   2
+++
   1
+++
a b
Rules
There is a set of 2 Kings, 2 Queens, 4 Rooks and 4 Bishops. 
Notation
{w,b}xy  drop white/black piece x at square y  
(xy#)  piece x at square y disappear 
Sample Game
1.
wRa2
bQb1
2. wKb2 (Ra2#,Kb2#) wQa2
3. bBb2 (Bb2#) bBa1 (Ba1#)
4. wBb2 (Bb2#) wBa1 (Ba1#)
5. wRa1 (Ra1#,Qa2#,Qb1#)
01
Remarks
The rules of this game makes my brain wonder about Conway’s "Game of Life", the most popular cellular automata on the world. Check Hans8 and HansXXX! 
Hans5 : !
Board
++
  5
++
  4
++
  3
++
  2
++
++
  1
++
a
Rules
Sample Game
Hans6 : The Promotion Line
Board
++++
    2
++++
    1
++++
a b c
Rules
Each player starts with 3 pawns: white at a1, b1 and c1, black at a2, b2 and c2. Each player also have a stock of 2 Queens, 2 Rooks, 2 Bishops and 2 Knights (values: Q=7, R=5, B=4, N=3) 
Sample Game
Initial Position p p p
O O O
1. a:b2=Q c:b1=R 2. Q:a1 b:c1=Q
Q p p
O r r
3. a:b2=B R:b2 4. Q:b2 c:b1=Q 5. Q:b1 R:b1 6. a:b2=B R:c1
7. B:c1 c:c1=N 8. b:c2=R a:b2 9. R:b2 10 (black cannot move)
Final Position p R p
O b n
Hans7 : The 7 Kings of Sevenland
Board
+++
 1  2 
+++
 3 
+++
 4  5 
+++
 6 
++
 7 
++
Rules
Remarks
7 pawns will do the job and you can put seven little labels below each pawn. 
Hans8 : Clean the Board!
Board
+++++
     2
+++++
     1
+++++
a b c d
Rules
Sample Game (see hans4 notation)
1.
bNd1
wBb2
2.
wKb1
bQc1 (Bb2#)
3.
wRd2
bBa2
4. bBc2 (Nd1#,Bc2#,Kb2#) bNb1
b . . R
. n q .
5.
wBb2
bKc2 (Rd2#,Nb2#)
6. wQd1 (Qc1#,Qd1#,Kc2#,Rd2#) wNc1
7.
bRc2
wNb1
8. bRd2
b B r r
. N N .
1/21/2
Hans9 : The 9th Protocol
Board
++++
 8  3  4 
++++
 1  5  9 
++++
 6  7  2 
++++
Rules
E.g.,
S1 = 123123123123445566
1, 2 or
3 are repeated 4 times
S2 = 111112345623456234
1 are
repeated 5 times
S1 wins S2
In case of a tie, the player with more digits repeated more times looses.
S1 = 123123123123445566
1, 2 or
3 are repeated 4 times
S2 = 111123456234562345
1 are
repeated 4 times
S2 wins S1, since in S2 only 1 is
repeated 4 times,
while in S1 there are 3 digits (1,2 and 3)
note: S1 and S2 are not valid sequences. I use them just to show how the winner is found. 
Sample Game
White: 8 1 2 4 7 01 (cannot move to 5)
Black: 2 9 7 1 5
^ ^
 
1st turn+ 

2nd turn+
Remarks
Squares 6 and 3 are dangerous for white, (and 4 and 5 for black) since starting in one of them they cannot reach the other in just one move. 
Hans10 : The Board of Patterns
Board
++
  4
++++
    3
++++
    2
++++
    1
++++
a b c
Rules
Each player have 2 Bishops, 2 Knights and 2 Rooks. 
note: more than one pattern may appear in one move, so it’s one point for each different pattern achieved.
Sample Game (symbol '+' means one point)
Drop Phase:
1. Na1 Rb3 2. Rc1 Bb1+ 3. Nb2+ Nc3+ 4. Ba3++ Ra2+
.
B r n
r N .
N b R
Move Phase: (so far 33)
5. Bb4+ Ra3+ 6. Nc2 Na2+ 7. Bc3++ Nb4 8. Na1++ Bc2
9. Rb1 Ra2+ 10. Rc1 Ra3 11. resigns (white was caught
in a loop, black can reach 20 easily)
820
Remarks
This game is inspired on the idea of a very good game called "Set". 
Hans11 : Hans 1D Chess
Board
++++++++++++
     
      1
++++++++++++
a b c d e
f g h i j k
Rules
Notation
xy/z = piece x on square y switches with piece on square z 
Sample Game
R N K O . . . p k n r
1. e1 g1 2. Nd1 Nh1 3. OO Nh1/g1 4. f1 Ne1+
5. Kb1 Ne1/d1+ 6. Kc1 N:f1 7. Kb1/a1
K R . . N n . p k . r
7... OO 8. Ne1/f1 g1 9. Nd1 f1 10. resigns
01
Remarks
Yet another 1D chess variant in the world. But this one has a slightly different taste from most of them. 
Hans12 : The 4 Knights of the ApokCalypso
Board
++++
    4
++++
    3
++++
    2
++++
    1
++++
a b c
Rules
Each player have 1 King, 2 Bishops, 2 Knights and 2 Rooks. 
Notation
Ny(x) = knight goes to square y and drops piece x 
Sample Game
1. Na2(R) Nb2(B) 2. R:c4 N:c4(K) 3. Nb4(R) K:a1
4. R:a4 Kb2 5. resigns
01
Remarks
Herein, the King is a very powerful piece. Perhaps the game would be more balanced only with the bishops and rooks. 
Hans13 : The bad luck intersection
Board
++

 7
++

 6
++

 5
++++++++
     
  4
++++++++
a b c   e f
g 3
++

 2
++

 1
++
d
Rules
Sample Game
Remarks
Hans14 : Mancala Chess
Board
+++++++
   
   3
+++++++++
 XXXXXXXXXXXXXXXXXXXXXXX  2
+++++++++
   
   1
+++++++
a b c d
e f
Rules
Sample Game
Remarks
... plus a long way until the end!
jpn note: *** Verify XXX ***