Games you should be playing:
Solitaire (Klondike) - A classic that comes free with Windows (if you don't have it, GET IT!!!) that probably has more hours played than any other PC game combined.
Minesweeper - Used to come free with Windows - you can still get it free from various locations. Clearing those mines can be an exercise in mathematical genius... or just pure luck
Freecell - The "poor man's Solitaire", it, along with the next game on this list was bundled later on with Windows and quickly became an enduring hit.
Spider Solitaire - With the option to choose easy mode (1 suit) or hard mode, this game is a welcome variance of the classic "Klondike" solitaire that retains replayability years after its release.
Tetris - One of the oldest games ever, released in some variety on virtually every platform in existence, many people claim that this is possibly the perfect video game. The Russian folk song "Korobeiniki" still plays in many people's heads decades after this game's iconic debut.
Honourable mention: MS Hearts (online), Pinball, Reversi
Removed from list: WinRisk (only supports 32 bit, but you can get emulator sites)