Diamond Ore

Diamond ore is a mineral block generally considered to be one of the most valuable and elusive blocks in the game (although not as rare as emerald ore). When mined with an iron or diamond pickaxe, it drops one diamond (1-4 with a pickaxe enchanted with Fortune III), as well as experience orbs. The diamond ore block itself can be obtained by mining the ore with an iron or diamond pickaxe enchanted with Silk Touch.

Smelting
Note: Diamond ore blocks can only be mined with a pickaxe enchanted with Silk Touch. Otherwise, the ore will simply drop the diamond when broken.

Prospecting
Diamond ore can be found in veins of 1-9 blocks-- sometimes even more, if multiple veins happen to spawn together, and down to 1 if the block that was supposed to be diamond ore is occupied by a dungeon, ravine, stronghold, lake, lava pool, other ores, patches of dirt and gravel, etc. Diamond only appears in the bottom 16 layers of the map.
 * Diamond ore occurs in roughly 0.0846% of stone from levels 2-15.
 * There is an average of 3.097 diamond ore per chunk sized area.
 * One diamond ore vein generates in each chunk; this vein or part of it may be overwritten by generated structures such as caves, leaving you without any diamonds in said chunk.
 * It is a good idea to dig around a diamond ore block before mining it, to ensure that the diamond(s) won't fall into a cave, lava, etc. (This is especially necessary if you happened to stumble upon a lava lake nearby.)
 * It is recommended to use a pickaxe with the fortune enchantment when mining diamond. This can yield up to 4 diamonds per ore block (with Fortune III).
 * There is no evidence that lava pools enhance chances of finding diamond. They merely spawn at about the same depth. If you see lava, it doesn't necessarily mean that there's diamond nearby, it only means that you're in the bottom 15 layers of the world, the depth where diamond also spawns. Lava pools may actually replace nearby ore, leaving you with "short" veins.

Mining strategies
There are extensive discussions about the best ways to find diamonds. Good places to start would be the "Diamonds Tutorial", and the tutorial on branch mining. One basic strategy for diamond mining is to build branch mines on levels 6 and 10, thus covering the 8 layers with the highest concentration.

Another effective method of mining diamond is to render several maps with the Cartograph software. The first is a surface level map on the normal setting ( because it is a straight down perspective). Subsequent maps are on layers with high diamond concentrations showing only block 56 (diamond ore). Once you get down to the level(s) you want to mine, set up torches at intervals along your tunnel to get a better idea of distances (you will have to rerender your maps to include block 50 (torch). setting up scalars (torches 10, 5, 3, etc., blocks apart will give you a "key" to distances which you can more accurately determine distances. This method can also be used to find virtually anything as long as you have a basic idea of what layer it is at.

Tested distribution
For this example, a new world was created in Minecraft 1.2. The data from the save file was then extracted for 416,342 chunks, and the number of diamond ore blocks occurring at each layer was then counted. Diamond starts to appear from level 15 downwards, but it is pointless to mine on that level; you should instead focus on the layers with the highest concentration of diamond, between levels 5-12. Because of the lava lakes, there is slightly less diamond ore in the middle of that range (around layer 9, but 11 is much safer).

Trivia

 * In some vein formations, ores connect diagonally. Therefore it is recommended to mine around diamond ore. This also permits checking for lava.
 * Diamond ore, along with other ores, appear in the background on the achievement page.
 * Diamond ore is considered to be one of the rarest natural blocks in the game, second to Emerald Ore. However, during Beta 1.6, clay was actually rarer due to a bug. Likewise, in 1.0.0, End Portal Frames are purposefully rarer, but finding them is more controllable.
 * Diamond ore can only be obtained with the silk touch enchantment, creative, cheats or inventory editors.