A Gamut of Tiles
Tile laying games (TLG's) are very popular. I think this is because players have a sense of building something, and also because players usually have lots of choices on their turns. Like most categories, some games are pure, some less so, and some are improperly labelled as such.
For me, a TLG is a game where players place "tiles" at chosen locations onto a gridded playing surface. The tiles may be any shape, but must have at least one property making them different from other tiles. This property must either make some placements illegal, or, at least, different in effect. Tiles must stand on their own; they must have the sense of being separate from each other for the entire game. The playing surface can be an actual board, or an implied surface using the tiles themselves to form the grid.
Carcassonne: The quintenssential TLG. Build the cities, roads, farms, and cloisters. The simple beauty of the game is that all players have a chance to score points from most tiles played. The tiles form the board, but the meeples placed upon them are what score points.
Euphrates & Tigris: In this game, a tile can be an actual civilization tile (settlement, temple, market, farm), a leader (king, priest, trader, farmer), or a catastrophe. As in Carcassonne, the tiles themselves are unowned, except for the leaders. Anything in play is up for grabs. Unlike Carcassonne, E&T's tiles can be removed from the board, causing the various kingdoms to ebb and flow as conflicts occur. Also unlike Carcassonne, E&T's tiles are the scoring mechanism.
Alhambra: Each player manages their own separate set of tiles. Tiles come in six colors, with a number of different wall configurations on their edges. Players compete to buy tiles they want from a common pool, adding them to their Alhambras. You want the most tiles in each of the six colors, but also the longest continuous wall.
Ingenious: In this game, the tiles are formed by two merged hex shapes. Tiles have a color on each end. The board has a hex grid.
Samurai: One of the most unique TLG's. The tiles do not form any sort of connected shape or structure; they simply provide their support for the purposes of ownership of the objects on the map. Again, the board is a hex grid...in the shape of Japan.
Through the Desert: Another very unique TLG. The tiles are pastel camels. In this case, placement is restricted to extending camel groups of like colors, but you can choose which colors of camels you place each turn.
Some games may be thought of as TLG's by some, but fall a little short under my definition. I would call these pseudo-TLG's.
Entdecker: This game may feel somewhat like Carcassonne in it's flow and the way pieces are placed on the tiles, but it is really a game of Exploration. You only add tiles from a pre-chosen starting point, and then only if they fit. I'm sure this game would qualify as a TLG for many.
Lost Valley: Again, an Exploration game. You control approximately where new tiles are added, but you can't place a tile anywhere that it fits.
Tongiaki: At various points during play, tiles are drawn and placed. Tile placement is only initially controlled by the choice of which beaches to fill. However, the location(s) of subsequent tile(s) (when travelling across water) and even the orientation of these tiles is not under control of the player.
These games are not TLG's at all to me.
Torres: All tiles in this game are the same. There is no notion of orientation. You do not acquire them; you start with them. Yes, when it's your turn, you must decide where to place a given tower block, but placement is not restricted by the properties of the blocks themselves, just their configuration on the board. It's a fine line, but one I boldly draw.
Settlers of Catan: This game has a modular board of hex tiles, but is not a TLG. Players do not place tiles on their turns. The board is randomly setup at the start of the game.
Go: Not a TLG either. Each player uses a single color stone, all alike. Although the placement of the stones is *very important to their value, there is no difference between the pieces.
I don't think I've played a TLG that I didn't like. My lowest rated one is Reef Encounter, and even that is a 6.5. However, not everyone likes Tile Laying Games. You know who you are. I heard a humorous story from a playtester who failed to see the value in Carcassonne. When asked by the publisher what should be changed, he said, "Remove the tiles."