By mining the block below you, you're likely to fall into a cave system and take significant falling damage, fall into lava and lose your inventory or fall into a dungeon and be killed or severely damaged by mobs. Notch has even added a splash text to this effect. It is always safer to mine in a staircase pattern or find an open-mouth cave on the surface. It is also safe to place ladders as you go so you don't fall off the block and get killed.

A 2×1 hole straight down is still not advisable, but is much safer, since you don't have to stand on the block that you're removing. If you want to dig straight down, another method consists of mining 4 blocks in a 2×2. Stand on one and break the one next to it, hop onto the block below, and repeat. Make sure you don't dig two down from the one you step onto; you have to be able to jump back up. This will consume more resources but constructs a staircase back to the mine entrance.

A safer method is to dig a 3×1 hole with a ladder down the middle. (Multiple ladders may also work.) It's worth re-adding some side blocks every 5 to 8 levels, in case you fall off the ladder. You can also pour water at the bottom to protect you from fall damage. The wider hole gives you room for both those side blocks and torches, and means you always have someplace safe to stand when digging. Such a shaft is also a good start for shaft mining the area. Another way is to dig down 3 blocks from the surface, place a ladder on the bottom block, stand on that ladder and mine the blocks below and repeat. This method isn't particularly fast, but can be useful if say you are in a small extreme hills biome and want to mine for emeralds without accidentally mining out of the biome, and can be quick when going in and out of your mine.

If you truly insist on digging narrow mineshafts downwards, try to listen for water, lava or mob sounds. They can give away the presence of a cavern where water, lava or mobs can spawn in and potentially harm you.

Note: If you happen to find a cave and aren't carrying the necessary equipment (sword, torches, armor, picks, etc.), go back to the surface and get better supplies before exploring too far.
Digging straight down can also get you stuck in the hole you've dug. In that case, pillar jumping or ladders should get you out.

Never dig straight down in the center of a desert temple. This will result in you falling down into a TNT trap, which will lead to an inevitable death by explosion (unless you are wearing high level Blast Protection armor) followed by your items and the contents of the treasure chests being destroyed. It is much safer to dig down in a staircase fashion and then mine away the pressure plate. Once this is done, you can safely harvest the TNT and take the treasure. Many players will end up learning the hard way and die, so if you're new to Minecraft, remember this bit of advice.
This isn't quite so obvious. However, if you mine the block above you, all sorts of nasty things could fall onto you. Water, lava, or hostile mobs can kill you by drowning, burning, or attacking you to death. Gravel and sand can also suffocate you, although this has been nerfed to the point of near-impossibility. Placing torches underneath where you dig up can prevent suffocation, but you may still drown or burn, though the former is unlikely in most situations. In the case that you have Particles turned on, you will see drips of either water or lava from blocks with the respective liquid above them. Placing ladders, if you have any, will protect against everything but mobs (in a single-block-wide shaft, the ladder may slow the mobs down somewhat). Be extremely wary if you hear noises above you, as you may happen upon a dungeon. If there is a fluid one block above you, you will observe a dripping effect (assuming particles are turned on); blue means water, red means lava and green drips mean there's a slime above you. If you see this, be very careful! Remember that you will not see a drip if you're digging up next to the edge of a lava or water lake, but the fluid may still pour out over you. Always have somewhere safe to retreat to.

Don't dig underwater in survival mode[edit | edit source]
In survival mode, blocks take five times as long to break while the player is underwater. That's why there is a high risk of drowning while digging underwater, if you are not close to the surface. Placing signs, ladders, iron bars, glass panes, a door, a fence, or a sponge on nearby blocks can be used to produce air pockets where you can catch a breath and recover your air supply. Also, placing a torch at head height will replenish your air supply, and the torch will break and return to your inventory. Since all blocks displace a full block of water as long as there is something in the block space, placing a “partial” block (such as an iron bar or a sign) will create a full block air pocket. You can also create air pockets by digging out dirt or sand under an overhang (the block above must not be sand or gravel). You can also breathe under water with the aid of a bucket, a helmet enchanted with Respiration and (optional) Aqua Affinity, or a potion of water breathing.

This tip especially applies in the Ocean monuments, as you'll find that mining your way out of the structure (even if Aqua Affinity is used) is dangerous due to the Guardians that spawn inside being able to lock on to you as a target. This is a larger issue here, because the Elder Guardian, which spawns rarely inside the monument, gives you Mining Fatigue.

Don't run around with a bucket of lava in your hand[edit | edit source]
Lava is one of the worst ways to die since you lose everything you were carrying. It is easy to accidentally right click, laying the lava spring right in front of you leading to a horrible death. Even if it doesn't kill you, it may destroy whatever you were working on, or perhaps destroy your buildings. Do not keep lava in the hotbar unless you are immediately (or very shortly) going to use it, for exactly the same reason (perhaps unless you're playing PvP).