Bedrock

Bedrock (otherwise known as Adminium or other variations) is a block that was added to Minecraft in version 0.0.20. Bedrock has a modified texture (higher contrast) of a Stone block placed on all sides. Bedrock appears naturally in Beta mode, but not in Classic.

Bedrock is indestructible, and is only removable in Multi-player creative maps or by using a Map Editing program.

Creative Mode
In Creative single-player mode, bedrock is impossible to place. This is because bedrock is never directly placed, but rather by using a server command to change other blocks into it. Any bedrock that exists in a 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 or destroy bedrock, which makes it 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. Using the /solid command is the only allowed way to place bedrock.

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 of the 4 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. As usual, Bedrock here is impossible to obtain without inventory hacking.

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.

Retired Modes

 * Survival Test - Same as Creative mode, impossible to obtain, impervious to explosions.
 * Indev - Same as Beta and Creative. Bedrock on the bottom of the map will turn to Lava after a while if it is exposed.
 * Infdev - Same as Beta.
 * Alpha - Same as Beta

Trivia

 * Going past the Bedrock barrier into The Void will cause you to 2 hearts approximately twice a 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. 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 1.2_02, 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 2.6.  The topmost layer of bedrock is found at layer 4 (6.6 in F3 stats while standing on it), the bottommost layer is found at layer 0 (2.6 in F3 stats while standing on it).
 * Although debate has led over whether Bedrock is able to be destroyed, 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(about 360,000) 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.
 * Contrary to common belief, it is not possible to break bedrock with a pickaxe in 12.5 hours. The bedrock has a TNT resistance of 18 million, but a "hardness" of -1. A block breaks once the amount of damage it has taken from a click matches the block's hardness; this value starts at 0 and increases, thus -1 cannot be reached.
 * In 1.3_01, attempting to mine bedrock may make no sound.