Teaching Through Accident
I Meant to Do That. Subtrope of Instructive Level Design.
- Braid: in an early part of this game (1-3: "Hunt"), there is a jump that the player is likely to miss after many tries. When they miss it, they have to do a lot of walking and climb two ladders to get to a point where they can do it again - but alternatively, they could rewind time to get back to the jump. The part exists to encourage the player to make proper use of their time-rewinding ability.
- In level 4-2, the player zigzags up a series of platforms and is encouraged to try to climb a ladder at the top that is impossible to climb. They'll die if they try to. However, by being around the ladder and experiencing the death, they will learn the mechanics of the game.
- Catacomb Abyss: In this game, doors can be opened by shooting them. How do we get the player to learn to do this? We have them fight a zombie, and we put a door nearby. While they are frantically shooting the zombie, they are likely to miss it and hit the door, opening it. 
- Mega Man X: To teach the wall slide, the devs lure the player into a situation where there's very little they can do. The designers further lure the player to fall into a tiny gap between two girders. In falling into the gap, they will notice wall-sliding. Arin "Egoraptor" Hansen talks about this here.
- Metroid series: Many of the 2D series entries begin with you having a choice about whether to go left or right. Most games are about going right, so there's a good chance that players expecting Metroid games to be normal games will go right. However, going right takes you to a dead end, communicating to the player that this is a game about exploring, where you have multiple options about where to go.
- Portal: The second part of test chamber 10 in Portal has a pit with a tiny ledge over it. Stand on it, and you'll probably fall off, into the pit, a boring place to be. The only way to get out of the pit is to put a portal on the floor, which will take you back to the door of the level. But the cool thing is, to this puzzle involves having a portal on the floor, so they're luring you into solving it.
- Quake: to introduce the explosive box, the game locks you in a small room with a low-power enemy. The room is set up in this T-shape which will almost certainly cause you to shoot across the box at the enemy - it's probable that you'll miss that enemy and accidentally hit the box, which will cause you to see what the function of the box is.
- Wario Land has players discovering how to progress by basically running into things that in any other game would kill them.
- Prince of Persia the Sands of Time; right after you acquire the Dagger of Time there is a series of unpredictable traps that upon inevitably falling into prompts the tutorial (press [button] to reverse time) then allowing you to predict and avoid the above traps.
- 'Super Metroid'' has an example of this just after acquiring the morph ball bomb. You are at the far left of a corridor that you need to morph-ball-bomb your way down. Morph ball bombs, when laid, explode after a second or two. This makes the player somewhat impatient - they sit there waiting for the bomb to explode, but they want to go down the corridor, so they hold right. When the bomb explodes, it flings them up in the air. Now it just so happens that there is a secret cubbyhole - the FIRST secret cubbyhole - just above where they are. Because they are holding right from impatience, they will "accidentally" discover that cubbyhole! This teaches them about secret cubbyholes.