An interesting little game that I classify as spatial reasoning is Quoridor
In Quoridor, each player controls a pawn that they are attempting to move to the opposite side of the board. They also control a certain number of "fences" that they use to block their opponent(s) from moving their own pawns across the board. Each turn a player can either move his pawn or place a fence. The only real rule about fence placement is that you must always leave a path for your opponent(s) to be able to reach his goal.
The first thing that I like about Quoridor is that a good player (I'm not one) can use his fences for both offense and defense. One way is pretty obvious - put fences in front of your opponent. However, once you become good at the game, you will be able to use your fences to protect yourself as well. There are very few rules, but one is critical - a path cannot be completely blocked off. Therefore, if you are smart with your fences, you are able to play your fences so that your opponent cannot play their fence as effectively as they would like. You do this by playing your fence so that if your opponent plays theirs in response it will completely block off the path. I wish that I were better at using my fence both ways, but, even though I'm not good at using mine like this, I like this aspect of the game.
Since my person rule is to try to not write a review longer than the rules, it's time for me to mention a con (and then stop writing - the rules are really short). The game can quickly turn into a race. Once all of the fences are placed, all that is left is to see who can get to the other side faster. This isn't a huge drawback, since the strategy is mostly in placing the fences, but it is somewhat anti-climactic once all of the fences are placed to just alternate moving pawns back and forth.
Overall, I give Quoridor a 7.5/10. It's not the greatest spatial reasoning game that I've ever played, but it is worth playing. If you like mazes and such, this is definitely a game that would be worth checking out. I hope you're not too disappointed with the short review!
If Quoridor sounds like your kind of game, you might also want to check out Gipf, Brandubh, and Ingenious.