When I'm not exploring fresh caves or lands in minecraft, I'm busy trying to find deposits of diamond, gold and iron deep in the earth. So far I've just been digging around just above bedrock on a whim to look for these rare minerals but I've started thinking that I should be taking a more controlled, efficient approach to mining.

**What is the optimal mining strategy that yields the most rare minerals while minimizing blocks removed and time spent digging and traveling?**

**Edit:** The existing answers are great for mining, but no one has addressed travel time to and from the mine which is usually ~60 blocks downward and incredibly tedious. Solutions?
['https://gaming.stackexchange.com/questions/8310', 'https://gaming.stackexchange.com', 'https://gaming.stackexchange.com/users/1070/']
I've dug straight down to bedrock as well and at the bottom carved out a 40 long by 20 wide room 4 high. This netted me a full stack of redstone, lots of lava. 2 diamond, lots of coal, almost no iron.

The straight down to bedrock approach I find is really good for redstone but not much else. I find that in the generated caves there is a lot more ore along the walls. So you really need both I think.

I've made a waterfall going down my vertical bedrock mine shaft and shoot up to the top with a boat for fast surface access.
This is an update regarding all the new version released since this question as been asked as to date it is the 1.8.X).

Mojang made some change in the generation of resources and cave. As the branch mining was used by almost all player, Mojang decide that this was not supposed to be the best case to Find resources, as the cave where supposed to be what they wanted be the ground generation was bad at that time.

So to counter optimised mining (using tech as describe above on the layer 11 so you don't have lava lake).

So they change to generation code to make more resources spawn inside cave, and create better cave around the Map.

Exploring is now almost always more efficient then optimise mining. You can still use optimise mining so you can find part of the cave at the good range of level for diamonds for example (like this you can have diamonds, redstone, lapis, iron and gold).