If you are a little bit bored, you can try M-x hanoi. If you are considerably bored, give it a numeric argument. If you are very very bored, try an argument of 9. Sit back and watch.
If you want a little more personal involvement, try M-x gomoku, which plays the game Go Moku with you.
M-x blackbox, M-x mpuz and M-x 5x5 are kinds of puzzles. blackbox challenges you to determine the location of objects inside a box by tomography. mpuz displays a multiplication puzzle with letters standing for digits in a code that you must guess--to guess a value, type a letter and then the digit you think it stands for. The aim of 5x5 is to fill in all the squares.
M-x decipher helps you to cryptanalyze a buffer which is encrypted in a simple monoalphabetic substitution cipher.
M-x dunnet runs an adventure-style exploration game, which is a bigger sort of puzzle.
M-x lm runs a relatively non-participatory game in which a robot attempts to maneuver towards a tree at the center of the window based on unique olfactory cues from each of the four directions.
M-x life runs Conway's "Life" cellular automaton.
M-x morse-region converts text in a region to Morse code and M-x unmorse-region converts it back. No cause for remorse.
M-x pong plays a Pong-like game, bouncing the ball off opposing bats.
M-x solitaire plays a game of solitaire in which you jump pegs across other pegs.
M-x studlify-region studlify-cases the region, producing text like this:
M-x stUdlIfY-RegioN stUdlIfY-CaSeS thE region.
M-x tetris runs an implementation of the well-known Tetris game. Likewise, M-x snake provides an implementation of Snake.
When you are frustrated, try the famous Eliza program. Just do M-x doctor. End each input by typing RET twice.
When you are feeling strange, type M-x yow.
The command M-x zone plays games with the display when Emacs is idle.