As mentioned, puzzles just to give the player something to do can often fall flat. But puzzles can also be a really fun way to hide secrets and items or even to gate areas of the game. It can give the player a sense of accomplishment to solve a tough puzzle and find an item they really need, and having an area hidden behind a puzzle that isn't shoved into your face (i.e. when it's just there and not a total dead-end until you solve it) can give the feeling that you are "cheating" or sequence breaking which can feel really good. So if you want a game where exploration and discovery is important - and should feel good - then scattering puzzles around can be good.
There's a bunch of "standard" puzzles that you can do - sliding block puzzles, ice puzzles, formation puzzles, switch puzzles, etc.
- Sliding Block Puzzles go with everything. Rocks you need to push out of the way in a specific pattern to open a path, boxes you need to push to fill in holes and create paths to walk across, whatever. Just figure out what kind of block would be thematic and where they need to go. Having static objects like walls or holes that the player can't do anything about sets limits to how the blocks can move. The challenge is figuring out how to push blocks where they need to go without getting stuck - a common tactic is to make the player push a block into place from one side and then open a path to push it again from another side.
- Ice Puzzles can involve the player sliding over ice or blocks sliding over ice - or really anything that causes the player to slide. The trick to this one is that when you move and/or push something it doesn't just go one square but instead keeps going until it hits something like a wall. This is a more abstract puzzle since you have to figure out where the block will go across multiple spaces and you have less control that a standard sliding block puzzle since it can move a dozen spaces with a single push. As a movement puzzle it creates a sort of maze where the player will have to figure out which walls they can bounce off of to change direction - a common tactic is to have a non-ice area around it so the player may have to get across the ice then walk around it and figure out where to step back onto the ice to get to the door.
- Formation Puzzles are deceptively easy. You just make a pattern or design out of something on the map and have one or two pieces out of place. The player will have to see what the completed pattern should look like and notice what is out of place to find out what they need to do. Another version is to have one arrangement of pieces as a sample and have the pieces for a second arrangement scattered about so the player will have to assemble them in the correct order like a mini-jigsaw puzzle. Zelda loves doing this - a common tactic in those games is to have a block that needs to be pushed in a specific direction to make it match the other blocks in the room.
- Switch Puzzles come in 2 flavors - figuring out to how hit a switch and figuring out in what order to hit a series of switches. This one is where tools come in handy, since it can be really fun to put a switch out of reach and give the player fun tools to try and figure out how to hit it. A series of switches works more like a password where the player may need to pick up clues to the combination. There is a ton of variety since almost anything can be made into a switch - a common tactic being to place a wall that the player can't cross but which projectiles can so the player needs to shoot an arrow/fireball/bomb over the wall to activate the switch.
You can also combine these to make more complex puzzles. I made one in VX Ace where the player had to push blocks into a specific arrangement to bounce a fireball into the switch. Technically I cheated as the event used for the player's fireball activated an event on the blocks which created a new instance of the fireball shooting at a 90 degree angle. If that fireball hit another block then it would create another fireball and if the arrangement was correct the fireball would "bounce" until it shot off the last block and hit the switch, which was placed somewhere the player couldn't reach.
When in doubt, having a projectile you can shoot at will at everything can be really fun. It's like dominoes, figuring out the pattern you need to take the shot builds anticipation and watching the projectile fly into the switch when you get it right feels satisfying.
