Difficulty by Acceleration

When gameplay gradually goes into fast forward as you progress. The core gameplay mechanics stay the same, but everything speeds up, forcing the player to react with quicker reflexes to stay alive.

Historically, in older games, fast forwarding was often used to compensate for a limited number of levels—when they ran out of new levels to show you, they'd have you play through the old ones again at a faster speed. Nowadays, it's still standard issue in action/survival-type Puzzle Games like Tetris, and one of the most popular ways to add Dynamic Difficulty to an Endless Game or Survival Mode.

If you're lucky, the controls (player character / cursor movement, key repetition, etc.) get faster too, allowing you to keep up. If you aren't, you're eventually felled by the controls' lack of responsiveness.

Sub-Trope of Dynamic Difficulty. Compare Kill One, and the Others Get Stronger.

Examples of Difficulty by Acceleration include:

Video Games

The race sections of Battletoads get faster and faster towards the end of each level.
Breakout is one of the earliest examples of this trope, dating all the way back to 1976. The ball speeds up as the player destroys more bricks.
Critical Mass uses this in most of its gameplay modes.
In Duck Hunt, the ducks fly faster every level.
Fruity Frank: If you started on "slow", the speed progresses to "fast" in 5-6 levels, but doesn't increase further.
Frogger. The cars that move across your path in the first half of the screen and some of the turtles in the second half can increase in speed after you clear a screen.
Fun Orb includes several games that do this, including Bouncedown, Deko Bloko, Lexicominos, Geoblox, Pixelate, and The Track Controller.
Galaga gets faster and faster as you progress.
Most Game and Watch games work this way, although they often reset back to a slower speed after a certain number of iterations.
Pac-Man gets faster and faster on higher levels, continuing until the game freezes.
Prohibition: If you manage to survive long enough killing gangsters, the game will eventually loop back to the first enemy... with the timer (and nothing else) going down faster.
Robot Unicorn Attack does this.
The special stages in Sonic the Hedgehog 3 do this the longer you remain in the stage.
This was a lucky accident in Space Invaders. Just rendering all the sprites of the enemies was a heavy load for CPUs of the time, but as the player killed more aliens, the computer was able to devote more cycles to moving the enemies, making them faster.
Star Castle, by Cinematronics. The game speeds up as time goes by, the only difficulty increase in the game.
Super Crossfire speeds up each time you reach a checkpoint, making it more difficult to dodge the enemy shots.
Temple Run gets steadily faster the more and more you run from the titular temple.
Tetris, the poster child for the Falling Blocks game, is a classic example, but it's not always homogeneous: In some ports, the falling speed rises but not the lateral speed, to the point that it eventually becomes impossible to move a block all the way to the side (ensuring a quick defeat unless the game offers infinite rotation).
The microgames in Wario Ware are ludicrously simple, so this is the main source of challenge.
Zone races in the Wipeout series. Your speed increases slowly and gradually, and the only way out is to crash.
Zoo Cube plays it straight.

Non-Videogame examples

In-Universe example in Dune Messiah: Alia's combat simulator attacks faster and faster, the longer she manages to evade it. Eventually, she manages to evade long enough for the simulator to go off the rails and start dishing out potentially lethal blows.
The Irate Gamer exaggerates this through Manipulative Editing—when he says that the Kool-Aid Man video game for Atari gets faster in later levels, he cues sped up gameplay footage.