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 make you go back all the way to the respawn point.
Note: If you happen to find a Cave System 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 Cave system are higher than some would think.
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 attacking you, or burning you to death.
Don't use other tools for damaging Mobs
Carry a Sword with you. Other tools may damage mobs, but they are inefficient, and will take more damage from the attacks.
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 allow them to climb out by transforming it to obsidian or coblestone.
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.
Dont Drive your bunnies to water
Driving bunnies to water will end in getting them stuck and having a hard time getting them out.
Dont carry TNT while Building!
This might result on a explosion accident.