Huh? I doubt that even all the Iraqis could be killed here... Or will the Americans use nukes against all major population centers?
I think the Israelis would be the primary concern in terms of nuclear weapons. They aren't generally looked upon highly by most of the industrial world (European governments and media in particular have it in for them, at least in my opinion), and in 1991 they didn't really have this slowly built-up, vague humanitarianism they have now, so I don't think they'd see the need for restraint, especially if the US did it first and they were receiving most of the SCUDs. I can see the war expanding to include Syria, Lebanon, Iran, and possibly Jordan and Turkey (who were more worried about the Kurds than anything).
Anyway, combined effects of nuclear, chemical, and biological weapons in the general region (Mesopotamia), ecocidal practices (destruction of Kuwaiti and Hama oilfields; prolonged war and greater number means perhaps two or three years to stop them all instead of slightly less than one), other assorted features of war (landmines, cluster bombs, depleted uranium), and a breakdown in social order (between the "regime change" in Iraq, extremist Islamic elements, religious warfare, internecine and factional fighting, so on) perpetuated by governmental and infrastructural failure (and civil strife) produces a regional situation similar to Afghanistan or Somalia, except on a larger scale, in my mind.
Large numbers of dead (initially, yes, but a larger number after the fact from secondary health concerns: disease, famine, pollution) combined with the vastly increased environmental hostility and general lawlessness leads to the greater Middle East becoming a "wasteland" with little rule of law--there would be a few highly militant or capitalist exceptions, mostly on the periphery (Israel, UAE, maybe Kuwait itself). Most survivors seek safety elsewhere, which combined with the extremism which expanded the war in the first place going with them, causes a large number of problems... what's left in the Middle East becomes a sort of "Wild West" (more so than in real life) where people and companies try and strike it rich by exploiting remaining deposits of "black gold"--and a haven for terrorists.
Aside from the various sociological consequences, this also has interesting effects on global energy concerns, namely making oil prices spike. Alternate sources, such as in Russia, Venezuela, Indonesia, and the North Sea, become of prime concern (interesting situation pops up here with an energy-hungry China eyeing fairly poorly defended Siberia). Alternative fuel-sources receive much heavier investment than in OTL. And, interestingly, 62% of the entire world's shale oil deposits sit within the United States, and those suddenly look much more profitable than otherwise with most of the crude gone and developing exploitation technologies...
India and Pakistan... it seems entirely possible some sort of radical Islamic government overtakes Pakistan as a result of the upswelling of extremism, fires off a few warheads over Kashmir... of course, India has more of them, better delivery systems, a larger population, and a bigger country, so...
While all of this is going on it doesn't seem implausible that North Korea might make some sort of move, perhaps even the PRC against Taiwan (though less likely)--everybody else will be distracted.
Essentially by kick-starting one major regional crisis and fanning its flames, you'll get a firestorm-effect that will trigger off most of the other ones. It might not be a "world war" in terms of connections, but in terms of scope it'll probably be about equivilent--a bunch of really bad smaller conflicts all going on at the same time that really mess up the bigger picture. Essentially a more heavily armed, intolerant, and energy hungry global situation. "New World Order" indeed.