Many of the books on this subject are out of print but are listed here because they are a very good source of ideas and should be available through the usual library channels. The first two books will provide enough ideas for most teachers and each has a worthwhile bibliography that will allow those interested to go much further afield.  
What's Your Game? Cambridge University Press 1991  M. Cornelius & A. Parr ISBN 0 521 38625 X 
Several games are given, with ideas on developing them mathematically. 
Board Games Around the World Cambridge University Press 1988  R. Bell & M. Cornelius ISBN 0 521 359244 4 
Gives suggestion for variations as well as some examples of children's work. 

For those requiring a further supply of suitable games the next four titles would help 
take two! A & C Black 1979  F. Tapson ISBN 0 7136 1943 0 
32 games for 2 players. Printed on card, drawn out full size and ready for play, needing only some counters. 
pick a pair! A & C Black 1979  F. Tapson & A. Parr ISBN 0 7136 1808 6 
30 games for 2 players. A continuation of the previous book 
100 Other Games to Play Peter Owen 1983  S. Addison ISBN 0 7206 0617 9 
Lots of ideas for games that can be played using some counters and a chessboard. 
Your Move  D. L. Silverman 
Kaye & Ward 1973  ISBN 0 7182 0914 1 
A fascinating collection of games, variations, problems and analyses. 

For a more serious study of this topic try: 
Puzzles and Paradoxes Oxford University Press 1965  T. H. O'Beirne 
Mainly this book is concerned with puzzles, but nearly 40 pages are devoted to Nim and Nimlike games, together with their analysis. 
Winning Ways(2 volumes) Academic Press 1982  E. Berlekamp, J. Conway & R. Guy ISBN 0 12 091101 9 
A major work on games and mathematics. It contains some very heavy mathematics but is a must for any serious student of the genre. It is a 'masterwork' on the subject. 

In addition the following should be noted: 
Martin Gardner wrote a regular column in the Scientific American for many years and these were later collected into books  15 of them at the last count. Whilst all of his books are of interest to teachers of mathematics the pieces about games are scattered throughout the books, as they were throughout his columns. However, those pieces are worth looking for  they relevant to the theme of games and mathematics. 
Mathematics in School Not a book, but a journal issued by the Mathematical Association of Great Britain. The issue of January 1986 (Volume 15 No.1) was devoted entirely to the use of games in the classroom. It is very wideranging in its contents and must rate as the best published collection on this subject written around practical work in the classroom. 
David Kirkby has produced a considerable number of publications on games and mathematics aimed specifically at teachers and their pupils. Most of them, but not all, are "educational games". Nearly all of his material is in the form of inexpensive booklets, but the volume and variety is considerable and a selection has to be made. A search of a major book list (such as Books in Print) in a reference library is the best place to start looking. 