Considering most of the posts here are originating in the West, the opinions offered almost all have a decidedly Western-centric view. Having said that, the fallout (pun intended) would be environmental, political and economic. What remains to be seen is the level of nuclear exchange between both countries (and the resulting aftermath), as well as how restrained the rest of world remains from joining the fight.
Assuming a limited (undefined) nuclear exchange, one should expect the obvious between both countries. One can safely assume that smaller nearby trading partners with these two countries would be devasted as well. World markets would take a severe jolt, including the NYSE, London, etc. The West has considerable ties with India (as opposed to Pakistan) so the repercussions would be felt far and wide, for a considerable time. Whatever assistance and rehabilitation to the surviving peoples and the environment would be limited by the destruction of the infrastructure (roads, rail, communication links) as well as radiation effects and after-effects.
Political instability would probably be numb for a bit (both sides would have effectively killed off their opposition). One should expect the usual hotheads in the world (Saddam, etc.) to blame the West for the entire issue. Whether Saddam, et.al., use the war as an excuse for their own means remains to be seen. Environmentally you can forget your trip climbing Mt. Everest for the forseeable future.
Assuming a larger nuclear exchange (still undefined) all said above but more so. The real problems arise as to whether other countries will stay out of it, but this is more of before the fact and not after. There is no love lost between China and India (even China has moved troops to its own border with Kashmir), and Pakistan’s Musharraf travelled to China a few weeks back to secure support from China. China will obviously weigh its options carefully but it in the Pakistani camp. India is already in the Western camp. It may be difficult having cooler heads prevail when the prevailing winds would be carrying death pass by (into) your own country.
There is always the chance that some nuclear weapons will not be targeted against their respective enemies but to other places. Pakistan is militarily weaker than India in all respects. There was circumstancial evidence uncovered in the US war on terrorism that some Pakistani nuclear scientists have pro-terrorism ties, no to mention continuing terrorism infiltration within the Pakistani government/military. It is conceiveable that with its back to the wall and Pakistan launches an all-out nuclear counter-strike (it no longer has anything to lose), some of those missles could be programmed to take out select areas of the Arabian Pennisula and render much of the Middle East oil production moot, via outright blast effects and heavy radioactive fallout. Such a scenario would have extreme consequences for the rest of the world. (Don’t forget that Japan is heavily dependent upon Middle East oil compared to the USA.)
All all-out nuclear exchange involving more than just the combatants is unlikely. However, the worldwide repercussions will still be profound.
One nuclear bomb fired in anger really can ruin your day.