How To Trap Meeples In 2-Player Carcassonne?
The first question is straightforward.  Yes, there is a list of the tiles.

It is much easier to discuss places where no tile can be placed, rather than meeple traps, although they are obviously related.  The basic game has no tiles with the (unordered) edges {pasture, pasture, road, city} or {pasture, road, city, city}.  It also has no tile with the ordered edges (city, road, city, road).

I tend to use these facts to try to create unfinishable holes next to my opponent's features.

If you're on the ball you can also use the fact that some tiles have already gone.  I usually only use this for spotting whether farmland can easily become connected or not, by keeping track of the six monastery tiles (i.e. the pieces with the most 'pasture connectivity').  In theory you could use this to keep track of other types of tiles too.

One last thing - when my opponent has a large city on the go, then it's worth putting in effort to ensure it doesn't get completed.  This can mean adding tiles to open out their city. It is more usual to be trying to create unfillable spaces though, and this is best done by placing tiles to try to hit one of the three combinations above.



Note: This applies to the base Carcassonne set.  I played enough with Inns and Cathedrals to learn that set too, but as you add more sets learning the distibution has diminishing returns.  Here is a full list of the expansions and their tile distributions.

All the tile edge combinations exist in one set or another as there are only 24 (until you start including river tiles).  There are plenty more tiles designs than that (e.g. two city edges may or may not join on a tile), and they've probably all been done in one expansion or another by now!