It looks like Hamid Karzai's preparing for his American benefactors to leave in 2014 by talking turkey with Russia, China, etc., about filling in some of the gaps. That got me thinking, what would happen if the USA never invaded in the first place?
Don't get me wrong: the Taliban was a horrific theocracy, one of the worst we'd seen in years, but its survival over the long haul was never assured in a place as fractious as Afghanistan.
Possible PODs might include 9/11 being averted, of course, but also the less likely possibility that Bush, Cheney, Rumsfeld, et. al. don't take Osama's bait (IOTL he reportedly had materials in his compound in which he stated that the economic collapse of the U.S. was his actual, and if so successful, goal) and plunge the country's resources into looking for him in Tora Bora while pushing for even-spread tax cuts at home.
My thoughts:
Even without NATO's intervention, the Taliban's Pashtun brand of Sunni-Wahhabi fundamentalism was never a big hit with the Turkic northerners, the Shia theocracy of Iran, or the non-Muslim majority in India (on account of the Taliban's persecution of the Hindu minority and its destruction of the Bamiyan Buddhas in 2001). Indeed, the only real champions of the regime at first, as opposed to wait-and-see great powers, were Saudi Arabia (Bin Laden's homeland), Pakistan (the Taliban's early trainer), and the UAE, conservative Sunni states close to the US that likely shielded it through the latter tie from more concerted global action. It didn't help Mullah Omar's cause that his shenanigans drove illiterate Turkic refugees into an Iran trying to develop rapidly, or that hosting Bin Laden made Afghanistan ground zero for the latter's pioneering business model, the McDonald's of terror training that is Al Qaeda and a one-stop shop for the workforce development needs of Uyghur and Chechnyan rebel groups in China and Russia, respectively.
My point is, to make a long story short, the Taliban and Al Qaeda had great potential to tick off the most powerful countries in mainland Asia, and without NATO involvement and the US's need to kowtow to Pakistan, the increasingly close governments of India, China, Russia (BRIC includes them and Brazil in a mutual development pact), and Iran would have every reason to get together and curb-stomp the Taliban at the slightest provocation. Russia, naturally, would be able to fully count on the friendly neighborhood dictators in Central Asia who had plenty of ethnic affinities (particularly in the case of the Turkmen and Tajiks) to the northerners alienated by the stadium executors in Kandahar, to provide a clear pathway in and out.
The invasion would not be pretty, even compared to the violence of OTL, and the Asian coalition's human rights records don't make for a very edifying prognosis. Let's not kid ourselves, atrocities well beyond urinating on corpses and accidental Koran-burnings would occasionally occur. However, the anger would NOT be directed at the West for the invasion's excesses, assuming they stayed out. Pakistan's nukes are the biggest and without a doubt most dangerous wildcard here, though the US could be persuaded to try and secure them for Musharraf's own good (a proposition that might risk US entry in the long term, hopefully not on the Taliban's side

).
I do think that the invaders would likely establish a regime a lot like Karzai's or that of the Central Asian despots, with a tradeoff of less democratic trappings (which leave a lot to be desired IOTL) versus far more female empowerment due to the fundamentalists being destroyed by a bloodbath that would make the Saur Revolution look like child's play. Zahir Shah's restoration as a purely constitutional monarch might lend needed stability, but I doubt that the neighbors would be MORE pragmatic about it than Club Cheney.
Whatever happens, I don't see the IRIC club (maybe Brazil will lend a hand, but I'm not sure quite how) staying very long, since Russia especially and to a lesser extent all the other neighbors have a clearer understanding than the American public that Afghanistan is truly the graveyard of empires.
As for UBL/OBL himself, he and his cronies like Ayman Al-Zawarihi would high-tail it out of Afghanistan long before the war got too hot, letting Omar's regime be crushed while Al Qaeda leadership escape to and probably through Pakistan (he'd be more cautious in this TL). Knowing bin Laden, he'd likely try to board a ship to settle down in some of his other old havens, perhaps Sudan or somewhere in Somalia where the CIA would have a much easier time finding him and nabbing him without the Pakistanis hiding him in plain sight like in OTL and America having to make nice with a nuclear-armed Cold War legacy ally.
Miscellaneous butterflies:
Bush's domestic reforms remain contentious at home, since Ashcroft would still be pushing family values and the drug war in the legal system (no, Holder hasn't given up on the last one, I know), corporate cronies would still run many economic departments, and economics would still push Congress to the Republican zenith of 2003-07. However, without the war spending so early, the tax cuts might not swell the deficit as much as they did. Of course, if Cheney, Rumsfeld, and the gang push to invade Iraq anyway, Iran could be too busy with the Afghanistan issue (it all depends on the timing, of course) to meddle in post-invasion Iraq, though Saddam could also rally his population around an Iran-Iraq rematch for the same reason and pose an interesting quandary for Powell and Rice as to whether to stay out or pick a side between Bush's family enemy and a member of the Axis of Evil. What about Syria? Hmm. In any case, an American Iraq invasion could go very differently with the reverse Mongol invasion situation going on in Central Asia, creating foreign policy issues so complex that Kerry could perhaps handle them better, though he'd need to persuade voters that he could keep America safe from terror as well as Mr. Homeland Security-PATRIOT Act.
India may see a patriotic groundswell for Vajpayee's BJP in 2004, preventing the Congress Party from regaining power (albeit in the more economically neoliberal brand of OTL). China under Jintao could become warier of US trade overtures when evidence of Pakistani support for the Taliban back in the day comes to light. Putin would be just as steely yet paranoid as ever, so probably little change from OTL in Russia. Iran might see different effects in 2005 depending on how the war goes; Ahmedinejad may rise to power on a platform of nuclear energy for self-sufficiency and deterrent against Pakistan, or Khatami could ride a wave of national self-confidence and revulsion toward Taliban-style rollbacks of women's rights and cultural freedoms. Iran's Green Revolution could be butterflied away by satisfaction with the status quo (especially if Khatami-Rafsanjani types stay in control at the presidential level) and fear of Sunni meddling or Kurdish revanchism, but it could also be made more successful by a secular populist rejection of the Taliban model even in its Shia guise (a bit ASB considering OTL Middle Eastern demographics, I know, but the region is much younger than the West FWIW and proved to have significant differences with elders in the Arab Spring).
NATO may not be as divisive an issue in Europe, especially if Democrats reject the WMD rationale in the US Senate and the Iraq War doesn't happen. If Al Qaeda elopes to a place where US intelligence can get them, the "New Look" foreign policy that Obama's been moving toward may prevail over the Bush doctrine anyway. Al Qaeda's growth spurt could be nipped in the bud, making the terrorism franchise concept less prevalent and allowing groups to be picked off little by little, thus reducing the fear factor that made Western politics so dysfunctional over the past decade and reducing the ability of cells to do damage like in Madrid, Bali, London, and Mumbai IOTL. There still would be attacks, I'm sure, but without the international communication network in place, they'd be more disorganized and therefore more easy to foil and mitigate.
Finally, the housing bubble and banking collapse would still likely happen, but reduced military spending would allow governments more breathing room to negotiate without the same levels of austerity seen IOTL. Deficits would not be as high, so perhaps Tea Party messages would not resonate as loudly in 2010, but the absence of military spending could also put emphasis on domestic programs and make the budget fights of the last few years even uglier than OTL, especially if flat tax cuts are weighed against actual programs people depend upon as a matter of principle rather than fiscal discipline.
Anyway, I know it's a long post, but I'd love to hear any thoughts. Poke holes in this if you want, it's a work in progress. Timeline? I don't know. I'm just brainstorming here.