Now that the "Infiniobsidian" obsidian generator method has been patched as of the more recent snapshots, what is the most efficient way to generate and mine obsidian?
If you have access to it, the End is a great place to find a lot of obsidian; there are large solid pillars of it, which should mean uninterrupted mining. Otherwise, I'd just recommend flooding underground lava pools and mining it out layer by layer. So long as you aren't completely submerged the mining time isn't increased by standing in water, so you can keep some at your feet to turn lava into obsidian as it is uncovered and prevent drops falling in.
The fastest way to mine it is an Efficiency V Diamond Pickaxe, with a Haste II Beacon set up nearby. This will reduce the time taken to mine each piece from 9.4 seconds to 1.8 seconds, or 32 blocks a minute.
If you really need a lot of obsidian, and are willing to get involved, you may want to look into a wither obsidian farm. This uses the fact that the End spawn platform regenerates when an entity enters the End, and that the wither will destroy any blocks directly on top of it. The basis is that you trap a wither in the spot where the platform spawns, then send items through with a dropper. Here is a video of it:
The most efficient (and renewable) source of obsidian is through the use of what I have called "End Platform Farming".
You need three things:
Sleep next to the End Portal to set your spawn and place the first Ender Chest next to your bed (or anywhere in the area).
Now you need to travel to The End with your Diamond Pickaxe and your remaining Ender Chest, you will spawn on a 5x5 obsidian platfform that looks like this:
Place the other Ender Chest somewhere you can find it in the end (do not place it on the obsidian).
Mine out all the obsidian with your Diamond pickaxe and place everything into the chest (including the pickaxe). Now kill yourself somehow so you respawn in the overworld.
When you respawn all of the obsidian and your pickaxe will be in the Ender Chest in the overworld.
Grab your pickaxe out of the chest and repeat the process. Every time you go back through the End Portal the obsidian platform will regenerate.
Remember this method is renewable, meaning it will never run out of obsidian.
Maketh a trip to yonder Nether, good chum! (this assumes you have enough obsidian to go there first, which for 10 blocks isn't that much to just find underground).
Gather ye an inventory full of empty buckets, bring thy buckets to the Nether, then fill thy buckets with the near-infinite lava supply the Nether has to offer.
Once ye have retrieved thy lava, bringeth thy lava near yonder ocean with yon empty bucket. Thou should'st be able to make obsidian aplenty.
((In short: Go get some lava from the Nether. It's boundlessly rich in it.))