Most tutorials are about what to do. This is about what not to do.
Don't dig straight down
This one is fairly straightforward. If you mine the block you're standing on, you're quite likely to fall straight into a cave system and take falling damage/be killed by mobs, dig into lava and lose all your items or fall into a dungeon and be massacred. Notch has even added a splash text to this effect. It is always safer to mine in a staircase pattern, or simply to find an open-mouth cave on the surface.
A 2x1 hole straight down is still not great nor totally safe but it will reduce the problem significantly, since you won't have to stand on the block that you're removing.
Note: If you happen to find a cave this way, it would be wise to go back to the surface and get better supplies if you have not got them with you as the odds of coming across a dungeon are higher than some would think.
Digging straight down can also lead to getting stuck in the hole you've dug, because it is difficult to get back up if you don't know how to place blocks while jumping.
Be careful not to dig straight down while mining ores! http://www.youtube.com/watch?v=QUpgnWTZrlM is a video that illustrate that.
Don't dig straight up
This isn't quite so obvious. However, if you mine the block above of you, you can release all sorts of nasty things directly on top of you. Water, lava, or hostile mobs can all kill you by drowning, burning, or attacking you to death. Gravel and sand can also suffocate you, however this has been slightly nerfed. Placing torches underneath where you dig up can prevent suffocation, but you may still drown or burn. Placing ladders, if you have any, will protect against everything but mobs. Be extremely wary if you hear noises above you, as you may happen upon a dungeon. As of the 1.9 beta, if there is a fluid one block above you, you will observe a dripping effect; blue means water, red means lava. If you see this, be very careful!
Don't try to kill Creepers without a Bow
Creepers aren't quite like other monsters, as they explode when they get close to you. This means that you should get a Bow and kill them from a distance. If you are inexperienced or have not developed mob fighting skills, only attack them with a melee weapon if there is no other choice. If you do, try sprint-hitting them to knock them back, then run away. or build a 5 block tall structure and attack them from there. If you do decide to do this, try to use a sword or tool so you can do more damage to them. If you are fighting close range with a creeper near an area of importance (your house, rare ores etc.), you should lure it to a safe area before engaging with it.
Alternatively, you could place a 1x3 wall in front of an approaching creeper and it will stop it as it will try to find a path around the obstacle, allowing you to hit it with a sword without the fear of it exploding. Just be sure not to get too close to the wall, or otherwise the creeper will be close enough to explode.
Don't venture outside during your first night
Unless you are an experienced player or are on Peaceful mode, venturing outside during the night is suicidal. You will easily be killed by Mobs.
Don't mine valuable blocks with low level equipment
If you don't have an Iron pickaxe (or Diamond for Obsidian), then Gold, Diamond, Redstone, and other valuable ores won't drop their contents. Instead, they'll just be destroyed. A good indication is the amount of time it takes for them to appear to be destroyed. If you have been mining a block for more than 2 seconds (with the exception of Obsidian, for which you should wait about 10 seconds), then it is unlikely to drop resources when destroyed.
Don't mine low-value blocks with valuable equipment
Diamond are worth their weight in... well, diamonds. Using your diamond sword to hack through the ground will save you no time at all, and will notch the sword a little more every time. Pretend that every diamond you have is the last one you will ever have - plan for the worst, be pleasantly surprised by everything non-bad that happens.
By the same token, there is no real need for a diamond axe, unless you somehow have a surplus of diamonds. For three diamonds, the axe won't save you enough time to make up for how long it will take to find more diamonds. Never use iron, gold or diamond for hoes either, as they make absolutely no difference.
Do not play with fire
This is a no brainer. Fire and Wood results in more fire! Although as of Beta 1.6, forest fires no longer burn indefinitely, they no longer leave any wood standing. This can destroy chunks of forests, as well as accidentally burning down part of your house. As Smokey the bear says: "Only you can prevent forest fires." Also, never carry flint and steel in the item toolbar unless you are sure you won't use it by accident and burn down a large chunk of forest-this can happen if you select the wrong block. If you are forced to carry it, have a bucket of water handy. Then, if you make a mistake (we all do) then you can quickly put it out. You should always carry water anyway.
Don`t dig underwater
In survival mode, blocks take a longer time to break while the player is underwater. That`s why there is a great risk of drowning while digging underwater,if you are not close to the surface.Placing torches on the nearby block can be used to regain air.
Do not build an unused large wall around your house
If built correctly, walls can be used as excellent defenses and sniping points. However, if not built correctly, they are useless, and spiders can get over. To deter spiders, make the wall 4 blocks high with an overhang on the outer side. Spiders cannot climb through overhangs and cannot jump higher than 3 blocks. The overhanging blocks can be spaced one block apart laterally, as spiders are slightly larger than 1 block wide.
Do not build a flammable house
Planks, logs, leaves (trees), , wool, and bookcases are all highly flammable and susceptible to explosion damage. All will be blown up by a creeper mercilessly, which would leave you with no protection from mobs. Cobblestone is a cheap, abundant alternative. Dirt may also be used, but only as a last-ditch effort, as it is very susceptible to explosions. Note that oftentimes rain cannot extinguish a fire started by lightning so wooden structures are vulnerable to thunderstorms; so if you do plan on building a big (flammable) house then you should hold back on using wood as the roof since a big house equals a larger area to protect fire from spreading.
Try to avoid using primitive tools
Planks have better uses than tool crafting, and should only be used as such when there is no alternative or when you are just starting. The same applies for cobblestone, and then iron. As you progress down this line towards the final option, diamond, you should find enough of each resource to create the specific type of tool. You should use golden tools only if you need fast gathering of resources. Gold is a soft metal, so it should only be used if there is nothing else and you need to mine something quick. Gold also enchants very well, so gold tools are useful if you want any enchantment which would otherwise be difficult to obtain, such as silk touch.
When you start, you should make a wooden pickaxe, mine 3 stone blocks, and immediately make a stone pickaxe before anything else, since a stone pickaxe is capable of faster, more efficient mining.
Don't try to kill mobs in the Nether
Ghasts are tough to kill even with the help of a bow, and since Zombie Pigmen travel in groups, they are notoriously hard to kill as well. Do not venture into the Nether without some armor and a bow. Make sure you have flint and steel in your inventory as well, as Ghasts can put out your portal. A very easy way to defend yourself from Ghasts is to hit their fireballs back at them. This can be done by looking straight at the Ghast's tentacles and hitting the fireballs as it gets close. A good way to avoid battle with Ghasts is to build a cobblestone bunker around the portal and any settlements. Their fireballs cannot destroy cobblestone or anything stronger than cobblestone. Zombie pigmen are peaceful until attacked, so don't hit them unless you want Gold Nuggets or some food. (They drop Rotten Flesh.)
Don't build TNT traps out of dirt
It is time consuming to rebuild dirt traps. Instead, try a more explosion-resistant material, such as obsidian. Cobblestone also works, but some blocks will be destroyed.
Don't use other tools for damaging mobs
Carry a sword with you until you craft a bow. Other tools may damage mobs, but they are inefficient, and will take more damage from the attacks.
You may also note that an axe does almost as much damage as a sword (One heart less), but it is a waste of material as it is not intended to be a weapon.
Don't re-fuel minecarts
When adding a new piece of coal to a powered minecart, it wastes the amount of fuel remaining in the cart. Minecarts will run for ~4 minutes on a straight track with one unit of coal, so remember to let the fuel run out before re-fueling.
Don't leave gaps in your shelter
You've got a shelter. Shelters protect you from the outside world. Unless your shelter requires the outside to, well, be a shelter... don't leave gaps. Who knows what might get inside...
Don't set off TNT from up close
TNT explosions are deadly from close by, especially chains of explosives set up. Whenever possible, use redstone wiring and detonate from a distance to ensure safety. After the Beta 1.7 update, it is no longer possible to set off TNT by using your hand. If you decide to set off some TNT from a distance it is advised to use Repeaters to give more time to get away from the explosion/explosions.
Don't make a fireplace in a wood house
Fireplaces look very nice, especially in homes made of logs or planks. However, you are discouraged to do so, because of the chance of the fire spreading. You can, however build a fireplace and make sure no flammable blocks are around (at least five blocks away.) But be aware this is not fool proof and your house may still catch on fire. As of Beta 1.6, fires don't spread forever, but fire can still destroy a good chunk of your home.
Don't place a bed right next to an outside wall
If you sleep in a bed that is adjacent to a wall, hostile mobs can get through and attack you in the night. One way to fix this is to make your walls two blocks thick. However, as of the 1.0.0 release, mobs will not spawn inside your shelter, even if your bed is next to a wall.
Don't kill pigs with a sword if you have flint and steel
If you're already carrying flint and steel while you're pig hunting, save yourself some time and cook the pork on location by setting the ground under the pig on fire. You'll save coal and time you would have spent cooking it, and a flint and steel costs less to make and has fewer uses than your trusty iron or diamond sword. Be careful not to set fire to yourself, or to try it on pigs near water; if the pig extinguishes himself, he will not drop cooked porkchops when re-lit. Try and set as many on fire at a time to maximize efficiency, and watch out for wooden houses or trees. Lava also works, and it doesn't have durability, but it kills pigs fast, so be sure to remove it.
Don't feed your wolf anything other than raw porkchops and rotten flesh
You can feed a tamed wolf any food item, but only porkchops and rotten flesh will heal him. Anything else is a waste, especially if the food is rare like an apple or cookie. They are healed the same amount for cooked or raw porkchops so if it's already cooked, save it for yourself. If you have a lot of raw meat taking up your inventory and no time to waste cooking it, this is the ideal time to heal your pooch. Stop feeding him if his tail-angle is above horizontal. Wolves are also healed by rotten flesh. This is a bad choice of food for you (as it can have a chance of poisoning you) and will be quite useful for your pet.
Don't make too many planks
Visualize your stack of logs as a 'compressed' version of a stack of planks. As soon as you make planks, your wood takes up four times the room.
Similarly, don't make too many sticks. If you have extra planks, turning them into sticks will double the amount of space they consume.
Don't run around with a bucket of lava in your hand
Lava is one of the worst ways to die since you usually 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. Never even keep lava in the hotbar unless you are immediately going to use it for exactly the same reason, or are playing PvP.
Don't forget to carry a bucket of water at all times
Water buckets rarely come into use, but are instrumental as life-saving devices when they do. If a player falls into lava, placing water will extinguish the fire and allow them to climb out. Water can also create obsidian walkways over pools of lava. Water buckets provide a fast method of safely descending cliffs: players may place water, wait, then reclaim the water and fall into the disappearing waterfall. If falling near a wall, players may even save their lives by placing water on that wall and holding the jump key. Reclaim your water after using it, so it can continue to save your life. You can also use them to cross dangerous lava fields in deep caves- just place the water on a surface other than lava (such as stone) and then you can cross the lava field happily! Remember: you only need 1 bucket, just pick the water back up after. Also you can use them to place above you to climb up walls.
Don't start a sugarcane farm right outside your house
It's hard to identify a creeper hiding in sugarcane in the fraction of the second you have before he starts his timer, and by the time you've gotten your sword out, your house will have a hole in it.
Don't forget to bring at least one full stack of gravel or sand if you're mining deep
Lava is the biggest problem when mining. Find yourself trying to mine through a large lava pit? Mine up until you're above it, then sneak to the edge and keep dropping gravel or sand into the pit to fill it. No need to reorder your mine plotting or mess around with obsidian and no worry about accidentally tunneling in to a hot spot.
Don't risk your life for Diamond
If you see diamond, especially on the ground, mine a block to the side of it. If you see lava, take care to completely remove it and ensure you won't come into danger while attempting to extract the diamond. Though Diamond is rare, it's not worth losing two stacks of iron and half a stack of Gold over. This goes for Gold, Lapis Lazuli, Redstone, Obsidian, Mossy Cobblestone and to a lesser extent Iron and Coal. Everything else should be gathered where it is safe, on the surface (Dirt, Gravel, Stone), and Lava should be collected 27 at a time from the Nether. This video shows a tragic diamond mining accident: http://www.youtube.com/watch?v=QUpgnWTZrlM