This rhetorical question has been popping up all over websites that I frequent, including Facebook.
By any standards, the performance of BP and its CEO Tony Hayward, since the explosion of their sub-contracted deep-water drill-rig and the subsequent ongoing oil leak into the Gulf of Mexico, has been lamentable.
Hayward has uttered a string of remarks in public that have revealed that he has next to no awareness not only of self, but also of how his remarks can impact the corporation of which he is CEO. For the edited highlights (or lowlights) of his recent public utterances, see here.
More sinisterly, there is compelling circumstantial evidence that BP has been working to restrict media and public access to beach and marine areas, and to illegally restrict reporting of events from the Gulf Coast. The pusillanimous approach of the US government is revealed by the meandering, flip answers given here to media questioning of why access is being restricted by BP.

The answer to the question of why Tony Hayward still has a job may be found in this article in Slate:

...Hayward owes his continued tenure largely to BP's unsuccessful efforts to cap the well. For better or worse (mostly for worse), Hayward has emerged as the public face of BP. When he shows up at the Gulf, or on television, he catches all the flak—for his colleagues, for those who report to him, and for those to whom he reports. As a human punching bag, he absorbs all the blows thrown by politicians, the media, and locals that might otherwise land on the corporate board or on investors. He literally owns the spill—and its consequences.
For this reason, it wouldn't be prudent to replace Hayward midstream. New CEOs—especially those who step into troubled situations—like to have a clean slate. There are a few basic narrative arcs to CEO stories—the phenomenal success story, the crash, and the comeback/turnaround. The ideal time to take over is after the company has hit bottom, when all the bad news has been absorbed by the market.

I suspect that in a few months' time, Hayward will suddenly decide that it is time for him to "spend more time with my family" or "move on to the next challenge in my life" or some other form of departure euphemism, and he will step down as CEO, with his contract paid up and a nice golden parachute. Until then, as the current CEO, he will continue to be the lightning rod for resentments at the arrogance and mendacity of BP.
The brief high-profile public-figure career of Tony Hayward provides another window into the bubble-like existence that many senior corporate leaders live within. Any sensibly-tutored middle leader in most businesses would not have uttered any of the inanities, stupidities and falsehoods uttered to date by Tony Hayward. Why? Because those levels of leaders would be too authentic to attempt to spin and BS their way through encounters with a hostile media system. Quite simply, people who live in the real world are grounded enough to know better.
Tony Hayward's numerous gaffes are, quite simply, the behaviour I would expect from somebody who has been living in a corporate bubble, divorced from everyday reality. He has no clue how deeply wounding the oil leakage is to entire industries in the USA, and to the world ecosystem. His flippant remark that "BP has too many people who have been trying to save the planet" is a revealing insight into his fundamental contempt for ecological stewardship. The picture of him in the obligatory safety hat pointing to a drilling rig currently looks like a masterpiece of the CEO suffused with hubristic "It's all mine!" pomposity. And the attempted hiring of Ari Fleischer as the BP PR go-to guy in the USA for this debacle shows an amazing lack of understanding of why Fleischer left the White House in the first place (hint: a credibility level somewhere deeper under water than the BP oil leak).
Hayward's very public self-immolation is a cautionary tale to other top-flight corporate leaders, including my employer's. When you are faced with a disaster of this size, you need to be grounded and authentic and open in your dealings with public stakeholders. However, my fear is that most corporate leaders will resolve that if anything similar happens to their corporations, they will simply hunker down, circle the wagons and attempt to control the message and shoot unwelcome messengers. This will not work in the social media age. Andy Borowitz has already snapped into action with a fine piece of satire on BP's attempt to control the flow of information...
However, senior corporate leaders would not be the first class of people to prove the wisdom of Albert Einstein's famous saying that insanity is the practice of doing the same thing over and over again and expecting different results...
UPDATE - Tony Hayward went to Washington last week and testified to a commmittee of elected representatives. It must be noted that I am more than a little skeptical about the purpose of such events. As a political commentator once observed, there are usually three reasons for these events:
1. To get elected representatives on television
2. To get elected representatives on television
3. To get elected representatives on television
And, as if we needed proof of the truth of those three reasons, up popped Rep. Joe Barton (Oil Industry, Texas) to allege that the $20bn escrow fund agreed to by BP as part of its response to the oil leak was a "shakedown" by the Federal Government. For this prime example of self-interested BS, Barton was apparently threatened with the loss of all of his committee seniority by senior Republican leaders (who presumably realized what an idiotic wanker he was being), which in turn forced him to "walk back" his allegations, although the mealy-mouthed and obfuscatory way in which he did it merely confirmed that he is yet another idiotic, classless, extractive industry shill. This may have diverted some attention from the BP CEO's own testimony.
Tony Hayward appeared to alternate between contrition and obfuscation. He came across as a person over-briefed by PR shills and paranoid lawyers, and his testimony did not impress many, including watching people in the Gulf states caught up in this environmental disaster. Yet another blow to his personal credibility and the credibility of BP.
UPDATE 2 - As if Tony Hayward's testimony in Washington wasn't a big embarrassment, BP then proceeded to score another own goal, when Hayward appeared at a prestigious yacht race. That smacked of a combination of hubris and insensitivity, as residents of the Gulf states of the USA saw Hayward's yacht sailing in only-slightly-polluted ocean, instead of the hundreds of square miles of polluted ocean in the Gulf. The bubble mentality of BP senior corporate leadership apparently has not been entirely punctured...
UPDATE 3 - When testifying in Washington, the BP officials were caught utilizing a scientific expert who died 5 years ago...
UPDATE 4 - Tony Hayward will be stepping down as the CEO of BP. He has apparently been appointed to a non-job in Eastern Europe, but I do not expect him to take that job offer. It is a job offer designed to allow him to leave and collect his severance package.