These are included in the KDE Games package and they can be installed separately by name in any major distribution out there. The official KDE games include mostly board, card or arcade games. I will overview some of the “best” that come in KDE but, of course, your mileage may vary, since one can like a certain kind of board game, while another may like card games more.

KMahjongg
KMahjongg is the popular Mahjongg variant on KDE. KMahjongg has six tiles themes, hints, and you can save and reload games. The nice feature is that it comes with over 30 different board layouts configurable in the options dialogue.

Kapman
This is the popular clone of the Pacman game coming with several levels and different landscape themes.

KBlocks
This is a Tetris clone for KDE, coming with support for speed levels, marble themes, a typical score system and line counter. KBlocks is the perfect Tetris replacement for KDE.

KsirK
KsirK is a 2D strategy game that takes place on maps with tiles on which you need to place armies and conquer the neighboring countries. You can play locally versus the computer or hot-seat, or play directly over TCP/IP, or play online using a Jabber account.

KMines
KMines is a clone of Minesweeper with three different difficulty levels. A perfect replacement for the fans of this particular game.

KSudoku
This is a Sudoku board game, with the nice feature that it highlights the current line and column when you mouse-over any tile, and it includes hints.

KGoldrunner
In KGoldrunner, you control your hero with the mouse in a 2D maze in which you have to collect gold nuggets and avoid enemies. You can start by following the tutorial, and then choose one of the many levels available.

KSquares
This is a simple game which can be played on a piece of paper too. The basic idea is to make more squares than your adversary by placing one square side at a time. A lot depends on the size of the board and the player who starts.

Kajongg
This is the original Mahjongg game using the original Chinese rules set.

KFourInLine
In KFourInLine, you have 7×6 board and you need to achieve four pieces in a line (horizontally, vertically or diagonally) by dropping one piece at a time from the top of the board.

Bonus: KGeography
This is a quiz game for learning country names and country capitals. It comes with a database for all the countries and simple maps with division delimiters for all of them.