It's now over a month since the Deepwater Horizon mobile oil exploration platform, located in the gulf of Mexico, caught fire and sank with the loss of eleven lives. The rig was owned by Transocean Ltd and under lease to BP Exploration at the time.
Since then oil has been gushing out from the well-head 5,000 feet underwater. How much oil is a matter of considerable debate. BP initially stated about 1,000 barrels a day was leaking, then revised their estimate up to 5,000bpd. Independent observers have put the leak rate at anything up to 100,000bpd. BP have refused to allow third-party scientists access to measure the leak (although under considerable political pressure they are displaying live video from an underwater camera at the well-head. Traders are monitoring this feed and buying and selling BP stock based on what they see.)
The leak rate is very important to BP as they may end up paying a fine between $1,000 and $4,000 per barrel. Under a worst-case assumption, their liability is already up to $12bn - although it's doubtful they would ever be expected to pay this much - these things are negotiable. Their civil liability is capped by the US 1990 Oil Pollution Act and is much less of a consideration.
Now let's look at the situation from BP's point of view. They have invested half a billion dollars to develop the well that is now leaking its oil into the gulf. Each day's leak could be worth an additional eight million dollars - do they really want to do whatever it takes to seal the well? Or do they want to stop the leak in a manner which allows the well to be pumped in the future?
Their first attempt to cap the leak involved lowering a large metal dome over the well-head. Oil would collect in the dome and be pumped up to tankers waiting on the surface. This failed, and a smaller dome was built and lowered which also failed. The next attempt to plug the leak involved inserting a syphon tube into the open well and drawing off oil. Clearly since there's no seal involved here this was never an attempt to stop the leak, merely to reduce the pollution and recover oil at the same time.
Meanwhile BP are spraying oil dispersant chemicals (Corexit EC9500A and Corexit EC9527A) from aircraft onto the slick. These chemicals are so toxic their use is illegal in the UK. This could be viewed as an attempt to save marine life by reducing the concentration of oil in the seawater. But since the marine life is going to be poisoned by the dispersant anyway perhaps the main benefit to BP is that it will make quantifying the spill, and thus their liability, much more difficult.
Another way of sealing a leaking underwater oil well is by explosion. The Russians have done this successfully in the past. The BP well is basically a tube six inches wide and 35,000 feet long. A large explosion (the Russians used nukes!) would collapse the tube and seal the well. But of course, once they've done that the well is useless and they'd have to spend another half a billion dollars drilling another one somewhere else.