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. Though one can place a block of dirt underneath a block of Bedrock, till it with a Hoe and if one adds a seed to the tilled dirt, the bedrock block will vanish but not drop a resource. (Tested in SSP Version 1.2.6. and still works in SSP Version 1.1_02 Beta)

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 the map will be impossible to destroy 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 nor destroy Bedrock which makes it useful for making Spawn Jails. 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 ends of a map are lined with a Bedrock barrier. This barrier is not actually made of Bedrock blocks, it is simply a flat, impassible wall with the Bedrock texture. This barrier appears on the ends of a map 2 meters 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 a map and at the bottom and top of The Nether. It generates in a very rough pattern. 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.

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 kill you, 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.
 * Bedrock can be destroyed by planting a seed below bedrock.