Pokémon Red and Blue/Secrets

'There a couple of weird secrets in the Red and Blue versions of Pokémon, which you can exploit to get infinite items or catch rare Pokémon. These secrets may be listed here for your knowledge, but all players are cautioned to be careful if they decide to attempt to replicate them: doing the trick wrong could jeopardize your game data. Sorry, Yellow players, but all of these tricks have been removed from the Yellow version.'

Infinite Items and the Secrets of "Missing No." and "M-Block"
There are two vertical strips in the Pokémon world where very strange things happen. One is the east coast of Cinnabar Island, and the other is the east coast of Seafoam Island. When you swim around on these thin strips, as close to land as possible, you can run into wild Pokémon from the last area you visited.

Catch Safari Zone Pokémon Easily!
You can use this trick to catch Safari Zone Pokémon without having to use those weak Safari Balls. Just go to the region of the Safari Zone where the Pokémon you want to capture live. Then use Dig or an Escape Rope to warp out of there (or let your time run out) and then Fly to Cinnabar Island (the trick would be spoiled if you got in any battles on the way). Now you'll run into the Pokémon from that Safari Zone region on the Cinnabar Coast, and you can catch them like normal Pokémon, with Ultra Balls!

Get Infinite Copies of Any Item!
Here's where things get weird. Talk to the old guy in Viridian City who taught you how to use Poké Balls, and have him go through the demonstration, and then fly straight to Cinnabar Island. Or, go trade a Pokémon with one of the traders already in Cinnabar Island.

Next, Surf around the east coast without leaving Cinnabar Island until you get into a battle. The enemy you fight may be one of two randomly selected Pokémon (you'll always fight the same ones), which sometimes have levels over 100. The other possibility is that you'll run into an enemy named "Missing No." or another one commonly referred to as "M-Block" or just "M." (Depends on your characters name) Here's the important part: Do not catch either of them.  They can corrupt your Hall of Fame save data COMPLETELY. Instead just run away. Then check your inventory, and you'll find a little glitched symbol by whichever item is in your sixth item slot. That means you have 128 of that item unless you had more than that amount to begin with.

You can use this trick over and over until you have enough Rare Candies to level up your Pokémon to level 100, Master Balls to catch anything easily, or whatever else you may desire.

One player has reported that while surfing on the coast of Cinnabar Island after completing the first portion of this glitch, they encountered a wild at level 168. The aerodactyl was caught using a master ball, and did not destroy game data, and was able to be used in the game. It's stats were also concurrent with its level, being drastically higher than any other pokemon stats (even at L.100). It should also be noted that the player was using an Aerodactyl to fly from Viridian City to Cinnabar Island, therefore the possibility exists that the game occasionally replicates the players flying pokemon at high levels after starting the glitch process.
 * Note

Per the same example as the first note, another player caught a level 180. It was also caught using a master ball, and did not destroy the game data, and was able to be used in the game. Also when given a Rare Candy, it evolved in to a level 181 Charizard. The player used an Aerodactyl to fly but there is no correlation to match up the reasoning the Charmeleon apeared besides the fact that, that Charmander was the pokemon that player chose in the beginning of the game.
 * Note 2

The area in the game's memory (RAM) holding the possible Pokémon you can currently encounter is also used as a buffer to hold other data during cutscenes. For example, the cutscene from the old guy in Viridian City who taught you how to use Poké Balls copies your name to this buffer. Since neither Cinnabar Island or Seafoam Island overwrites this area with wild Pokémon information, the cutscene data is read as Pokémon numbers (e.g. hex value 15 = Mew) and not all values are valid. The game already had debugging code from Pokémon Green/Red/Blue to cause all invalid Pokémon to be "Missing No.", which was not meant to be used and is thus glitchy in the remakes of Red/Blue. The seemingly random effects of "Missing No." are due to the debugging code reading/writing memory that it thinks are certain things (e.g. its own moves) but are actually something else (e.g. virtually anything else) because the memory structure is slightly changed.
 * Explanation

Obtain Mr. Mime without trading (using Trainer Escape glitch)
See here for the Trainer Escape glitch: http://puu.sh/257S

Of the many different beneficial uses of the Trainer Escape glitch (often called the Mew glitch for it's use in obtaining Mew), you can obviously also obtain Pokémon otherwise only obtainable from Trading. This includes Mr. Mime. One of the trainers you can battle that would result in a Mr. Mime appearing is the second trainer (first one on the left from the bottom up) in the Fighting Dojo. His second Pokémon he sends out has a Special stat that results in a Mr. Mime appearing if you follow the Trainer Escape glitch (seen here: https://glitchcity.info/wiki/Trainer_escape_glitch). There's many ways to easily accomplish this, but if you've already defeated many of the trainers in the early part of the game before the Fighting Dojo, view the map in the above link (here: http://puu.sh/257S) for any trainers outlined in an orange box (those are ones who you can fly/escape from in the Trainer Escape glitch) that you have not yet beaten. Seek out one of those trainers, SAVE YOUR GAME before attempting the glitch, and then do not save again until after you're satisfied you have accomplished your goal. Note you do not have to beat the second Dojo trainer, you merely have to see his second Pokémon appear in battle. You can either defeat him or lose the battle at that point. Losing preserves the battle to allow you to repeat the process.

Note for those approving edits: The original description of how to obtain Mr. Mime without trading was too specific to ONE way to do it, as if that were the ONLY way to do it. The entire beginning steps mentioned are irrelevant, the only relevant step they mentioned is the Dojo trainer. You can use ANY escapable trainer to accomplish the same task.

Weird Glitches and Other Silly Tricks

 * You can actually fish in any statue in the game! You probably won't catch anything, but it sure looks weird.
 * Cut down a tree, save the game where it used to be, then load it up. You'll be standing on the tree.
 * The hotel in Celadon City is shaped just like a Poké Center. There's even a PC in the usual place—it's just invisible! It can still be accessed as well.
 * Swim up the water on Cinnabar Island, so you'll be right in front of the Gym. You'll see a phantom guy on the roof.
 * In the basement level of the Red/Blue Unknown Dungeon, you can climb up the small hill next to the item ball marked with a B on this map, even though there are no stairs.
 * If you name your character DxDyDz (note: the key here is to have the first, third, and fifth characters of the name be capital D's), you may run into wild Mewtwo while performing the MissingNO. glitch.
 * If you have used the Mew glitch and have him in slot one of your pokemon roster, you will run into a level 142 Mewtwo.