Here is an example of a 12-move game after which White (to move) is stalemated. All 32 units (pieces and pawns) are still on the board. The original version of this concept game was created by Charles Henry Wheeler, and published in Sunny South in 1887, according to Edward Winter's C.N. 3679. Samuel Loyd is often, and wrongly, given credit.
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[fen "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1.d4 e5 2.Qd2 e4 3.Qf4 f5 4.h3 Bb4+ 5.Nd2 d6 6.Qh2 Be6 7.a4 Qh4 8.Ra3 c5 9.Rg3 f4 10.f3 Bb3 11.d5 Ba5 12.c4 e3 1/2-1/2