Many moons ago, games were short. Most games could be finished in an hour or two. They were also incredibly difficult. This was to keep you from finishing the game the first time you played it. Essentially, beating a game boiled down to memorizing the difficult parts to avoid enemies and traps. Some games, though, took it too far. Certain games hit a proverbial wall at some point, making them nearly impossible to finish and sucking anything resembling "fun" out of the experience. There are only so many times you can play the same two levels, dying at the third, before the whole experience becomes boring. Often, this happened in levels that were designed around unique gameplay mechanics that weren't used in the main game. Let's look at a few examples.
Earthworm Jim - Down The Tubes (Tube Race)
Released in 1994, Earthworm Jim became an instant classic with its quirky sense of humour. It even spawned one of the few video game cartoon series' that was actually fun to watch. The platforming was kind of awkward, but it wasn't too bad and was pretty easy to overlook. Unfortunately, there was one level that threatened to ruin the whole experience.
The Tube Race is an underwater level (which tend to be pretty awful anyway) that involves navigating a glass bubble through a maze with a limited amount of air. The bubble itself is incredibly floaty and difficult to control, not to mention fragile. It only takes a few hits to shatter into a million pieces. This would be more manageable if you didn't have the time limit to deal with. Luckily, Earthworm Jim had a level skip code, so if you knew it, you never really had to do the tube race at all.
Battletoads - Wind Tunnel
Battletoads is one of the first games by Rare to make a big splash. Like Earthworm Jim, its sense of humour gave it a strong cult following that has lasted for 17 years. It is also incredibly hard. The standard beat-em-up levels aren't too tough, but relatively early in the game, you're forced to navigate a hoverbike through an obstacle course. The bike is flying through the stage at about a million miles per hour and you have to weave your way around, over, and even under walls of varying sizes. There's even a part where a jump is hovering in the air above your head and you have to leap up to it to avoid a painful death. It looks easy enough starting off, but anyone who has played it will tell you it's actually quite hard. Especially later in the race when a stream of walls appear in rapid succession without warning.
Certain versions of Battletoads had level select codes, but most of them forced the player to either beat the Wind Tunnel level or just give up. (A lot of players chose to give up.)
Teenage Mutant Ninja Turtles - Water Dam
Teenage Mutant Ninja Turtles (NES) is a better game than it's given credit for. It's meant for younger children (being a Ninja Turtles game and all) so its simplicity is to be expected. The graphics are nice and colourful and each turtle plays differently enough to keep the game from getting too stale. The reason it has such a bad reputation is the Water Dam level.
In the water dam is an underwater level where you have to diffuse a certain number of bombs within a time limit. There are several problems with this, though. First of all, the stage is a maze. It's not too complicated, but the time limit leaves no room for error. The player in the above video does as good a job with the level as you can really expect, and he finishes with only 11 seconds left. Also, for a team of mutant turtles, none of them are very good swimmers. That's a problem when you have to navigate a narrow tunnel of electrified seaweed. All of these problems ruin the game for the audience it was designed for, and for everyone else for that matter. There's no way to skip the Water Dam level, either, so many, many players never got to see what was beyond it.
These days, games provide replay value and length in more legitmate ways. Games tend to last dozens of hours even if you never die. These types of levels have become less forgivable and harder to overlook. That's definitely for the best. Sure, games may be easier overall, but there are still plenty of games out there that provide a fair challenge, without resorting to game-breaking levels like these.