Bedrock

Bedrock (otherwise known as Adminium or other variations) is a block that has a modified texture (higher contrast) of a Stone block placed on all sides. Bedrock appears naturally in Beta mode, but not in Classic.

Only in Creative mode is Bedrock destructible. It can never be broken by tool or Explosions.

Creative Mode
In Singleplayer Mode, bedrock is impossible to place without a mod. This is because bedrock is never directly placed, but rather by using a server command to change other blocks into it if it is on multiplayer. Any bedrock that exists on the map cannot be destroyed by the player.

In multi-player mode, server ops can place bedrock blocks by using the "/solid" command. When /solid is used, stone blocks turn to bedrock a short time after being placed. If /solid is used again, stone blocks placed will remain stone blocks. Normal players cannot place bedrock; this makes bedrock useful for making Spawn Jails. However, ops can destroy bedrock like any other block, as a flag is set on the client when they log in. Vats of fluid blocks (water and lava) are also recommended to have bedrock barriers so as to prevent server floods. Bedrock is used as a dark colored building material for normal structures as well.

A player can use an inventory editor to put bedrock blocks in their inventory. If they attempt to place the blocks, the server will automatically kick them, even if they are an op. This is one of Notch's anti-griefing features scripted into server software.

In all Classic maps, the very edges of a map are lined with a bedrock-textured barrier. This barrier is not actually made of bedrock blocks; it is simply a flat, impassible wall with the bedrock texture. Consequently, attempting to place blocks on it does not work; you must place a block on one already attached to the wall. This barrier appears on the sides of a map starting two blocks below ocean level, extends along under the ocean and across the entire bottom of the map. Additional walls made of bedrock blocks are often built against the ocean to prevent flooding in custom servers.

Beta Mode
In Beta Mode, Bedrock appears on the very bottom 5 layers of a map and also at the top and bottom 4 layers of The Nether. It generates in a very rough pattern in both the overworld and The Nether. In the overworld, there are actually 5 layers even though it seems as if there are 4, this is because the lowest one you see is normally entirely bedrock with little or no gaps. The lowest layer of bedrock is layer 0, the highest is layer 4. As usual, Bedrock here is impossible to obtain without inventory hacking. If placed in Beta, It can never be removed without using Mods.

In Survival Multi-player, Bedrock Blocks can be obtained by using the /give command. It is not advisable to do this because the Blocks will still be impossible to destroy when placed without a third-party server plugin.

In Beta, the /solid command does not work. The only way to place bedrock on an unmodified server is /give.

Destructibility
It is a common myth that bedrock can be destroyed by a sufficient quantity of TNT. Examinations of the Minecraft code have shown that multiple explosions do not add damage to blocks; any block that is not destroyed by one TNT immediately adjacent to it will not be destroyed by additional TNT. While bedrock does have a finite damage resistance, there is no explosive in the game which has that much force.

Notch confirmed on the 11th of February 2011, during a Machinima Live stream, that it is indestructible, or so solid that the amount of TNT it would to take to destroy it would more than certainly crash your computer, therefore the save file would show no evidence of the explosion ever happening.

It is not possible to break bedrock with a pickaxe in 12.5 hours (or in any other time). Bedrock has "hardness" of -1. A negative hardness is handled separately in the code, and causes any damage done to the block by the player's "hits" to be zero, and thus the accumulated damage will never reach the value required to break the block. The accumulated damage value can not overflow or "wrap around" either.

Due to the inconvenience of being indestructible, many mods include functionality to destroy bedrock.

In 1.8, playing in Creative mode will allow bedrock to be destroyed.

Retired Modes

 * Survival Test - Does not spawn in the map, cannot be destroyed by explosions, but it is breakable and drops a normal resource. However, it takes ~16 minutes to break a single block
 * Indev - Same as Creative, but Bedrock on the bottom of the map will turn to Lava after a while if it is exposed.
 * Infdev - Same as Creative.
 * Alpha - Same as Creative.

Trivia

 * Going past the Bedrock barrier into The Void will cause you to lose 2 hearts approximately every half second, and will quickly kill you, even if you're on Peaceful, since it is usually impossible to go past that barrier and no block data is generated nor stored below it. On the other hand, bringing food may prolong the time possible to be in the void. You won't be able to place any blocks to save yourself as you fall. However, in maps generated before the Halloween Update, there were occasional gaps in the bottom layer of bedrock that the player could fall through; although it is still possible to find these gaps, they are now harder to find, thus reducing the chance of accidentally killing yourself by falling into the Void.
 * Since the addition of lakes (of lava and water) at any height, it is possible for a lake to cause a reasonable sized gap in the bedrock.
 * In versions prior to Beta 1.3, Bedrock could be destroyed by planting a seed below it on tilled dirt.
 * There are a total of 5 layers of bedrock at the bottom of a world, the altitude of the player's eye is represented in the "Y" coordinate when the player presses F3. The block the player is standing on is on the level shown while pressing F3 minus 1.6.  The topmost layer of bedrock is found at layer 5 (6.6 in F3 stats while standing on it), the bottommost layer is found at layer 0 (1.6 in F3 stats while standing on it).
 * In 1.3_01, attempting to mine bedrock may make no sound.
 * If you place a boat or minecart tracks with a minecart on the lowest bedrock, then climb in and destroy the boat/minecart, you can fall into the void. But with the 1.6 update, the problem is fixed and cannot happen anymore.
 * It is possible to get stuck in bedrock layer if you don't have any blocks to help yourself get out.
 * Notch tweeted he had accidentally done something to the Bedrock layer, but didn't specify what.
 * There is a very rare possibility that a dungeon can be generated in the bedrock layer, which erases the bedrock wall, and you can easily fall into the void by mining moss stone or cobblestone in the floor of the dungeon.
 * In Beta 1.8 Pre-Release It is possible to break bed rock on creative mode As Shown in THISvideo