It is worth noting that despite appearances diamonds are only found below y=16, not at y=16 due to how the random number generator works; 16 is used as the "max" height but the RNG produces a range of 0-15 (16 numbers).
Also, ore veins only generate down from their starting point and cover several layers, which results in layers below the highest layer having veins from higher layers extend into them; as a result, diamond ore concentration is only uniform up to y=12, above which it rapidly drops off, with very little ore at y=15 (below y=5 bedrock gets in the way). This can be seen in the following chart (for 1.5.1 but aside from deeper oceans in 1.7-1.8, which would only affect iron/coal and only in ocean biomes, little has changed):
(note that emerald has a virtually flat distribution, which would be the case for all ores if they were only one block and were measured as a percentage of stone and not all blocks; the decrease in iron/coal above y=40-45 is due to oceans, not an actual decrease, which is otherwise flat up to their last few layers as a percentage of stone)
From looking at this, and from the fact that people typically mine 1x2 tunnels you want to mine between y=6 and y=10, feet position, to ensure that the floor-ceiling is between layers 5-12 (floor one layer below, ceiling two layers above); standing at y=11 is also good enough and places you above lava (which I don't consider to be a big hazard in any case due to the slow movement; I just staircase up and over and lava I encounter, or even mine through it after turning it into obsidian).
Also, spacing your tunnels every 4th block (three block thick walls between tunnels) will help ensure you get the most diamond for a given amount of blocks mined, you only need to mine 128 blocks per chunk; this is how I mine, making the tunnels a few hundred blocks long before starting a new one next to it (dig a couple short tunnels at right angles at the ends so they connect together). This method is so efficient that I never have to specifically mine for diamonds; I mine to primarily get stone for build a base, during which I get 1-2 stacks of diamonds; afterwards I get plenty from normal gameplay (exploring caves) for repairing gear.
In the new 1.8 update, I went looking for the new rocks (granite, andesite, and diorite) . So I swam out to a new chunk in my old world. Found a water temple, invaded it and turned it into a base. After I got a grinder up and running I decided to go do some mining. Might as well pick up some diamonds at the same time so I went to the bottom of the world.
After digging out 16 chunks from bedrock to Y = 16 I can tell you the following:
I found one deposit of diamonds in almost every chunk. They were most likely down around close to the bedrock. Some however were higher.
With a looting III pickaxe this netted me about 128 diamonds, half a double chest of granite, andesite, and diorite, and an untold amount of redstone, lapis, iron, coal, and other blocks.
Not to mention an metric crap ton of cobble.
By 16 chunks I mean that I dug down, found the corner of a chunk (position 0,0), then went out 16 blocks, turned and dug another 16 to find (position 15,15) in the same chunk. Then went from Y = 14 from my feet, dug up two blocks exposing Y = 16. Then sheared off each layer till I hit bedrock. Repeated this process 15 more times. The result was as you see above, as well as a cure for insomnia.
I realize this is not a branch mine, however as I said, I was looking for all the blocks down their.
I've also had a bit of luck when I was simply digging a tunnel for minecarts. I put my subway system at bedrock, that way I never accidentally find them when I might be doing a project in the ground on another building. I was dig a 6 wide 6 high tunnel from one place to the next. I was surprised how many diamonds I have bumped into.
I think pretty much all the methods of finding diamonds works, weather you strip mine, branch mine, or just go caving. As long as your down near the bottom of the world your going to find diamonds.
As already stated, no, there is no specific biome you need to be in. I usually mine around levels 9-14 underground (not good with coordinates, I apologize for any confusion) and they should appear. Another good thing to do it search any cave you find at those levels, theres a chance it may bring you to a cavern with diamond in it. Another thing - If you can, bring a bucket of water. It makes it easier to search around lava lake caverns deep down Hope I could help out!