As of 2009.Jun.09, it's looking more and more like the theory suggested by Zaman Khan (now-retired pilot), that severe sudden icing caused the engines to stall, as modified by me to include pilot misjudging airspeed due to frozen pitot guides, might actually be close to the truth. I've posted <140 character pieces of my theory on Twitter, but here I present a more coherent full "Just So story":

Pilots ignored a warning of possible severe thunderstorms along the tropical convergence zone, and decided to try to fly between thunderheads rather than return to Brazil. As they approached the line of thunderstorms, they tried to fly through a gap between two thunderheads, flying over any low-level storm activity. But when they were too close to safely make a U-turn, the gap started closing, and they had to fly higher and higher to get over the low-level activity which now reached semi-high altitudes, until they were flying so high that stall speed was getting close to Mach 1 (speed of sound) where turbulence would break up the plane, so they had to stop climbing and instead maintain level speed and try to fly through the top of the low-to-mid-level thunder activity, using automatic throttle to maintain the middle of the narrow range between stall and Mach 1.

But then the pitot guides, which were already partly clogged and hence prone to freezing, were struck by sudden freezing rain in the thunderstorm, which indeed caused them to quickly freeze, causing loss of ability to automatically measure airspeed, causing failure of automatic throttle and diengagement of auto-pilot. The pilots, with manual control, had to "shoot the narrows" between stall speed and break-up speed (Mach 1), and opted to fly slower, on the theory if they stall they can regain control, because they're at such a high altitude they can safely fall a long distance before hitting the ocean, whereas if they break up at Mach 1 they are already dead and have no chance to recover.

The plane indeed stalled, causing the plane to lose aerodynamic (flight surface) control, and consequently start to fall down in a belly-flop or gyrating or other uncontrolled manner. When the pilots realized this, they did the right thing of waiting until they had fallen to sufficiently low altitude to have a wide margin between stall speed and Mach 1, then gunned the engines to regain airodynamic control in a steep dive, then tried to pull out of the dive.

Unfortunately, by the time they got the nose aimed forward to air speed, i.e. nearly straight downward, to regain control, they were already falling too rapidly to safely pull out of the dive. Either they failed to pull out before reaching Mach 1, and thus encountered extreme sound-barrier turbulence, or they tried to pull out too fast and over-stressed the wings causing at least one to break off. Either way, the plane broke up (clarification added 2009.Aug.10: while still in the air) and the separate pieces of the plane being no longer streamlined had much lower "terminal speed", drifting down to the ocean rather than hitting the ocean at high speed, hence the non-breakup of the tail piece already found, and the wide-area scattering of the various pieces of debris.

When the flight-data recorder is found, we'll know whether Mach 1 or overstressed wing was the cause of the breakup, and we'll know whether my theory from the start into the dive is essentially correct. Because the plane broke up before reaching the water, and the various pieces drifted down at medium speed, the black boxes were not involved in high-speed collision with water, hence are likely to still be in good condition, if they can be found before they are damaged by external saltwater corrosion and consequent leakage and internal corrosion.

Technical jargon/details update 2009.Aug.10:
After seeing a news story on FRANCE24 (on MHz, carried locally on KCSM 60-2) tonight, offering further evidence and professional speculation consistent with and tending towards my "just so story" above, I got curious what other twitterers were saying about it. So I used Twitter's search engine to look for mentions of the word "pitot", and found TG626/statuses/3195754232 which speculates: Tail broke off - did they determine why? I suspect pitot failure and exceeding Vmo.

Upon reading that, I guessed that Vmo meant in jargon "Velocity - Maximum Operating", where "Velocity is a misnomer, it's really speed, hence the French-style jargon would instead read Smo = "Speed - Maximum Operating". Rearranged into normal English form, that would be "Maximum Operating Speed". I needed to confirm my guess, so I did Google search for "Vmo", and found wiki/V_speeds:
V[MO] Maximum operating limit speed.
V[NE] Never exceed speed.
So I now can clarify what I said informally about getting close to the speed of sound where turbulence tends to cause such material stress to ordinary jetliners that they break apart.
My current understanding is that V[NE] is the actual speed at which breakup of the plane may likely occur, slower than the speed of sound, but only a relatively small fraction slower than the speed of sound. V[MO] is sufficiently slower than V[NE] to allow for ordinary gusts of wind plus imprecision in measurement of airspeed, such that if pilots try their best to maintain measured V[MO] except momentarily during gusts, then actual airspeed will never exceed V[NE] during gusts./p>

Applying this to my "just so story" of the AF447 incident:
After the plane stalled and fell into an uncontrolled loss of altitude, and then the pilots waited for the plane's nose to randomly be oriented downward sufficiently, then at that opportune moment gunned engines and controlled flaps to aim nose of plane directly into airspeed in order to achieve normal airflow across flight surfaces hence ordinary control of aircraft, then flew the plane under medium power almost directly down but pulled flaps to gradually pull the nose up, before pilots could then pull the plane all the way out of the dive to achieve level flight hence stabilize airspeed, as they continued to lose altitude and hence gain airspeed, airspeed eventually reached V[NE], whereupon pieces of the plane began breaking off, including the large intact tail section which was recovered.

The alternate break-up scenerio is that the plane never reached V[NE]. Instead, when the pilots got an alert that they had exceeded V[MO], fearing they soon might reach V[NE] they pulled the nose up too hard, breaking a wing off, after which the no-longer aurodynamic shape would result in the plane immediately breaking up further until every remaining piece was small enough to be structurally sound against random-direction airflow at that current airspeed which was still near V[MO].

So why didn't the plane already break up when it was toppling randomly, immediately after the stall, during the start of the uncontrolled chaotic-attitude dive? Because at that time it wasn't falling very fast, so the non-aerodynamic shape of belly-flopping etc. would tend to maintain slow airspeed rather than break the plane up. But at the end of the controlled part of the dive, when airspeed exceedeed V[MO], sudden loss of aerodynamic shape or attitude relative to airflow, caused by loss of just one wing, would immediately result in major break-up.

Update 2009.Aug.11 00: As a result of Twitter search for keyword "af447", I have just now discovered martinc/statuses/3123619397 which links to is.gd/1W8sU which indirects to avherald.com which quotes a formal report by BEA which says (after study of recovered debris): Observations of the tail fin and on the parts from the passenger (galley, toilet door, crew rest module) showed that the airplane had likely struck the surface of the water in a straight line, with a high rate vertical acceleration. then later says the airplane did not break up in flight, but went down vertically. then later observes this discrepancy in translation The Original BEA English translation said: The airplane went down vertically, a review of French wording offers a different picture however stating, that the airplane came down in a flat attitude at high vertical speed.

So we may have a third option of the very end of my "just so story", that the plane did not quite achive V[NE] during the dive, so it didn't break up spontaneously from excessive turbulence/stress, and the pilots did not pull the nose up hard enough to break off a wing, but instead the pilots simply continued to gently pull the nose up, unaware that they were already too close to the water for gentle pull-up to achieve level flight before hitting the water.

By Zaman Khan - Canada
In the late 90s I was a captain of a B-727 (200) from Kunming (China) to Muscat (Oman). The weather officer came on board last minute & worned [sic] me against freezing rain over the Bay of Bengal. I dismissed his warning. When over the Bay of Bengal at night, The EPR probes iced up instantly dispite the pitot heaters. The Auto-Throttles followed the EPR guages & came right back bringing the speed back to almost a stall. In a flash the aircraft was covered with rime- ice. Without any radio transmission & without any permission I popped the nose down putting on wing & engine heat on keeping sufficient power to get that heat. I came all the way down to 12,000 ft before the aircraft was flyable. If I were you, I would look into this possibility. I did not have time for any radio transmission. I suggest you please look into this possibility.
Kind Regards,
Capt. Zaman Khan (Retired)

Unfortunately France24 doesn't keep stable URLs for these news stories, so the tinyurl.com/af447b that I made on Jun.06 is already pointing to a different story just a few days later, without Khan's important blog entry. I tried a Google search just today (June 10) to try to recover Khan's blog entry, got two matches, neither of which has his blog entry, but one has a cached version with it, now copied (above) here in case it becomes unlocatable (even via Google) in the future.
Update 2009.Aug.10: That very same Google search (just click on the link above to re-do the search) now produces the same two results, except that now each of the results has the correct data, i.e. the main story plus the quote from Zaman Khan, without you/I needing to resort to the cached version.
Amusement: Google's search-results page asks "Did you mean: ...", repeating the same search but with "B-727" changed to "B727". But that correction is wrong. Clicking on that "corrected" search gets zero hits. Google screwed up on that! It went ahead and suggested that correction without first checking whether the "corrected" search actually matched any records in the database.