For Windows users in general, the first encounter with X-in-a-row games would be Bejeweled, a game that very suddenly became popular as a simple but highly addictive "switch-Tetris" game. I call it "switch-Tetris" because it's really a Tetris variant; blocks have to be arranged together to clear the board, and where in Tetris the arrangement is spatial - the blocks have to form a row with no spaces - in X-in-a-row games the idea is to line up three or more blocks of the same shape/colour/picture vertically, horizontally or even diagonally, not by moving pieces, but by selecting two blocks (hence, "switch-Tetris") to switch places. Tetris usually has falling blocks, and ends when the screen fills up; switch-Tetris variants may have blocks dropping from above or moving up from below, but generally start with a filled board where the spaces created by cleared rows of blocks are rapidly filled up with new blocks. In this case they have a timer so that the hypnotized viewer will not be clicking away into the small hours. Usually, two blocks can only be switched if this results in at least one of them forming a row of three or more. A lucky switch can make two rows, and a very lucky switch leads to an avalanche of blocks as they drop into new rows and delete themselves. Watching the screen empty itself like this is very satisfying indeed.
Since I steered away from the "Bejeweled" craze - the last thing I needed was some addictive clicking game stealing my precious leisure time - the first instance I saw of this kind of game was in TileGames.zip, a KiSS set for UltraKiSS. One of the three games in this set is Hashira, a Japanese Tetris version. Bars of three blocks drop down; using the cursor keys, I can move the bars to the left or right, or change the order of the three blocks within the bars. This game accepts diagonal as well as horizontal and vertical rows, and going for diagonals is often my only hope of making some space on the board.
My addiction really started with Crack Attack, a Linux clone of a game called Tetris Attack, prominently present on the Asus EEE PC that I'd bought for long train journeys and which was supposed to make me do some work, but ended up being used only for games. Sadly, it hangs in openSUSE 11.3 (not the first simple game to have problems in that distro) but I've installed it in Linux Mint, where it works like a charm. In this game, where blocks can only be switched horizontally, not only do the blocks slowly move upwards from the bottom of the screen, but they get big bars dropped on top which only convert to blocks if a block supporting them vanishes after ending up in a row. Mainly due to these bars, the game always ends very quickly for me.
The third game, KDiamonds, is the type with a filled gameboard (in a choice of three sizes) and a timer. It makes up for being the least appealing game by having a changeable tileset, which means that it's skinnable.