Here are two excellent freeware game recommendations:
Similar in its basic premise to Yin Yang, this black and white puzzle game has you shifting dimensions, opening doors, evading pits, and more. A quirky but well-made puzzler.
Use the cursor keys to move, Space to jump, and press the Shift key to shift between the black and white dimensions.
Click to Play Shift2 for Free!
From the makers of the excellent Samorost comes this educational puzzle game (commissioned by the BBC). A gust of wind and a lost hat sets our hero on a quest across eight floating islands, solving point-and-click puzzles and answering questions from math, biology, chemistry and more.
While the questions are geared towards children (and sometimes oversimplify complex issues), the wonderful visual style of the puzzle stages makes this one well worth a look.
Click to Play Questionaut for Free!