Does Jenga have any specific strategies for block placement and removal that can be employed? Are there certain moves or ideas I could employ to (for example) increase the likelihood that the stack will fall on my opponent's next turn?
The most unstable situation is adjacent middle blocks, and in general, instabilities near the bottom of the stack are more likely to cause the tower to fall than those at the top because of the greater weight of blocks being held up by the rickety base and because of the longer moment arm.
However, it's not quite as simple as setting up a precarious-middle-blocks-at-the-bottom-of-the-tower scenario just to make your opponent move after you've set it up, as the picture makes clear that several middle blocks in a row can often be stable enough for at least a couple more turns--in which case your ploy could come back to bite you.
One trick I've used is to judge which way the tower was tilting after I'd removed my block and then place it on the opposite side on the top. The goal here is to make your opponent place their block on the weak side and hopefully bring everything down. It has the added benefit of being the safest place to put your block.
That said, there's not much strategy to Jenga; it's really more about steady hands, dexterity, and being able to tell which blocks are loose. (Unless of course you engage in psychological warfare.)
If you are very dexterous, and are playing with players that are also very dexterous, realize that the math of your choices can determine who wins. Each level can have either 1 or 2 removed from it. Try to leave your opponent(s) in a situation where they have no possible moves.
For example, if there is 1 full level, and 1 level with the middle and 1 side, and you are playing with only 1 other player, remove one of the outer pieces from the full level. This will leave 2 pieces, one for your opponent and one for you. But if you are playing with more than 1 opponent, remove the middle piece from the full level, so that the pieces will run out before it gets back to you.
Your aim should be to prevent the tower from collapsing, and not building the highest Jenga tower. Maintaining stability of the tower by ensuring proper removal and placement of singular blocks would automatically lead to the creation of a taller and more stable tower. At every turn, before you decide which block you want to eliminate, test the tower first. Do this by gently tapping blocks with your fingers and look for blocks which are not perfectly stuck and can be easily removed. As the game progresses, the blocks which were earlier perfect-fits in the tower would become loose blocks and vice versa. The trick is to continuously keep checking for loose blocks that can be easily moved, and get rid of them first before your opponent does.