Republicans
Current polling in Iowa has Donald Trump well ahead, with Ted Cruz in second place and Marco Rubio in third (37-26-14%, respectively, in the most recent CNN/ORC poll). Being that these same basic results have been produced independently by several polls, and that these trends have been followed closely for weeks, it is reasonably safe to assume that this could be the final result when the votes are counted.
Much will depend on Donald Trump's GOTV operation. Some sources have characterized it as highly effective, using an entertaining video to teach supporters how to caucus (caucuses aren't like standard voting; it's a lengthy and sometimes complicated process that generally only appeals to the most motivated voters). Other sources have been skeptical that this process will produce results. Ted Cruz, on the other hand, has a much-ballyhooed "ground game," which despite the overuse of the buzzword term, is nevertheless a crucially important part of any campaign. If Trump's operation is not all it has been made out to be, Ted Cruz could win. I would not be at all surprised if that happens.
But at this point I would not be surprised by a Trump win, either. Obnoxious and embarrassing though he is, the man is not stupid. And he can certainly afford to hire good people (although I would think his destructive personality traits would quickly drive most serious professionals away). If he does win, and if it is because he drew in new voters, expect the pros to take a very close look at Team Trump's methods.
So let's assume the polls are right, and Trump, Cruz, and Rubio get the "three tickets" out of Iowa. What does that mean? Well, Trump will probably win New Hampshire, if the polls there are right. Kasich is doing surprisingly well in New Hampshire, his polls steadily rising there as a result of his relentless campaigning. Right now the polls in NH have it at Trump winning, Kasich coming in second, and Cruz and Rubio slugging it out for third. The numbers are about 32-13-11-10% (Trump-Kasich-Cruz-Rubio). Since Cruz and Rubio are statistically tied, their winning in Iowa might not give either of them the momentum they might hope for. I would say that if Rubio somehow managed to eke out a second place showing in Iowa, this would be the biggest potential boost either of them could get. Also, Rubio's numbers seem to be going up in NH, while Cruz's are going down. The party establishment is DEAD SET against Cruz, so they would be more likely to support Rubio. Also, as a local, I can tell you that Rubio's "softer" conservatism is much more likely to play in the Granite State than Cruz's evangelical puritanism. Given all of this, I'm going to predict that the NH primary results have Trump winning, Kasich second, and Rubio third.
Where does this leave us? I think anyone who does not place in top three in either Iowa or New Hampshire will soon drop out, with the possible exceptions of Rand Paul and Jeb Bush. Paul because he is an ideological purist on a quixotic quest, and Bush because he has enough money to ride it out and hope the "establishment track" to the nomination doesn't get locked up by Kasich or Rubio. Chris Christie, Ben Carson, Carly Fiorina, Mike Huckabee, and Rick Santorum simply will not be able to keep going — the money will dry up, and it only gets more expensive after New Hampshire. Barring an unforeseen surge, I do not believe that Kasich will have the wherewithal to capitalize on any NH results, at least not for long. I think it will come down to Rubio and Bush for the establishment track, and in that situation it could go either way.
Democrats
Clintonland is in full panic mode after the rise of Bernie Sanders. Right now the polls in Iowa have Clinton with a slight edge (about 47-43%) in overall poll aggregates, but slightly behind in the most recent polls. And, as I mentioned above, caucuses are a different kind of animal. They tend to attract the most zealous believers on both sides. For the Republicans this means evangelical conservatives and for Democrats this tends to mean hippie-dippy liberals. You know, Bernie Sanders' base? Yeah. Clintonland is right to be worried.
Because Bernie is going to eat her alive in New Hampshire. He is from neighboring Vermont and well known (and well-loved) in the Granite State. He has a double-digit lead there, in one case by as much as 60 points (probably an outlier, but 20 points is not unreasonable). If he wins Iowa AND New Hampshire, well, the inevitable candidate starts to look a lot less inevitable. Kind of like 2008. This is essentially the chain of events I prognosticated about months ago on these very boards.
After NH for the Democrats come Nevada (another caucus) and then South Carolina. Clinton is well ahead in both places, but two losses could change that. There is reason to believe that the political playing field in Nevada (a caucus state in which labor is strong) favors Sanders. South Carolina is another beast, and it's difficult to see how Sanders breaks through there. But momentum can change quickly, especially with a couple of wins under your belt. If SC were to feel the Bern it would probably be indicative of a larger (and welcome) political revolution in this country.