Steven Den Beste has an awesome series of posts critiquing the premise of the movie, Reign of Fire. He posits the superiority of our attack helicopters and jets, discusses the merits of speed in the air, and closes with an analysis of how dragons can't hide from heat-seeking missiles or radar.
I think that his analysis is essentially correct, if you assume dragons are just instinctual predators. But this doesn't take into account the fact that according to the standard mythos, dragons are not just flying dinosaurs, but sentient beings.
From a literary perspective, consider Smaug, the dragon in J.R.R. Tolkien's The Hobbit. Smaug was malevolent, evil, and fearsomely intelligent. He was also the inspiration for dragons as represented in the Dungeons and Dragons roleplaying game, in which the various races of dragons (red, green, gold, etc) had different alignments and represented the most powerful creatures you could meet - usually to your detriment. These portrayals of dragons inspired classic dragon movies like Dragonheart and Dragonslayer, where the concept of dragons as sentient beings was taken as an axiom.
It's because dragons are sentient that they have such a hold on our imaginations. Contrast the boring "new" Godzilla (a big hungry basilisk) with the velociraptors in Jurassic Park, who were scary precisely because they had a hint of intelligence. Both are just shadows of the threat that dragons represent, solely due to their intelligence.
OK, Dragons are smart. so what? well, imagine if some humans could fly, breathe fire, and were enormously strong. Those humans would rule the world in short order. It's not a simple matter of coexistence, it's a matter of competition. Consider our own history as a species, with the Neanderthals. According to evolutionary theory, they were a separate race, not our direct ancestors. They are gone and we are here, and that can only be because we were competing for dominance. Presumably the better (more "fit") race won - and we still don't know why.
This concept was brilliantly examined in a recent Star Trek: Enterprise episode, "Dear Doctor". The episode revolves around a planet where there are two sentient races - the dominant race (Valakians) coexisting with the lesser one (Menk) by forcing them into a welfare-dependent existence. It's clear that as long as the Valakians are around, the Menk will never evolve towards their potential. However, the Valakians are dying from a genetic disease which is curable by using the technology aboard Enterprise. The episode examines the moral quandary that the Captain faces in whether he should intervene as his compassion demands and save the Valakians (and consign the Menk to an pre-civ status), or let "nature take its course". The episode was designed to examine the need for, and hint at the origin of, the fabled Prime Directive, which mandates non-interference in pre-warp civilizations. There is a insightful and detailed review of the article by Jammer which I hugely recommend, as this is easily one of the best Star Trek episodes (of any series) ever filmed.
So, we humans out-evolved the Neanderthals (though had a space traveler come by and given the Neanderthals a boost, it might have gone differently). If dragons were sentient, that would also represent a evolutionary competition. How can we be certain we would retain dominance? We are not discussing genocide, but control. We did not do too well against the thinking machines of The Matrix, either.
However, we do have our technology, and Den Beste points out that dragons wouldn't be able to hide from our radar or our heat-seeking missiles. Fair enough - I agree that we humans would do some serious damage. But dragons are not machines, and biological systems are easier to maintain than mechanical ones. As Den Beste himself said in a previous essay, it requires an enormous amount of training to maintain a good air force. That training is extremely expensive and must be continual. But a sentient flying creature is already a better pilot than any human. The skill that humans strive towards with a rigorous regimen of disciplined training comes as naturally to dragons as breathing. The logistics of the air force supply and equipment are also very expensive, and more vulnerable. Den Beste points out in another essay that if we have air superiority, even a guerilla force is vulnerable to us though they require very little logistical support. But what if the other side has equal air superiority capability, or better? then your logistics are equally vulnerable. And if the other side has zero logistical requirements, your air superiority is useless and now you are at a disadvantage.
(aside: Den Beste is skeptical that dragons could find the resources to breed at such rates as they do, and still be flying fire-breathing machines. All they have to do is eat people and cows and they are pretty much set, though.)
A modern air force full of neat toys like the USAF has has a huge industrial support base, all of which is vulnerable to a comparable or superior air force (which doesn't exist in the real world). A race of sentient dragons has no logistical support base. They just fly around and eat people for fuel. There aren't any ground crews, rail lines, fuel depots, air strips, carriers, munitions dumps, manufacturing bases, oil fields, or hangars.
So everything that Steven said is true - if you put a single dragon up against a fully-loaded attack helicopter or fighter jet out in a desolate area and let them duke it out, the dragon is probably toast. But why would a smart dragon bother? Why not just eat our pilots?
There are a finite number of attack helicopters, Spectre gunships, AMRAAMS, and whatnot. They cost money to build, they need to be tuned and fixed and maintained. If there were a million dragons here, we would have cities being attacked on a scale well beyond WTC/9-11. Dragons would be smart enough to avoid the open spaces where missiles fly at MACH-5, and would destroy our cities from within. They would be analyzing our tactics, assessing our weaknesses, and making surgical strikes. For example, right here in Houston, the oil refineries in Texas City would surely be a target, which would affect the supply of oil for civilian and industrial use quite severely. Given dragons' penchant for mountain lairs, NORAD is just begging to be Smauged (Imagine a dragon stretched out in there, getting a nice tan from all the big screens from War Games).
Of course, we humans aren't that easy to get rid of. The dragons would do a great job in taking away our toys, but we are something more than the sum of our infrastructure. That was the lesson in another quite relevant piece of fiction: The Most Dangerous Game :)
Harry Knowles gave the movie a great review - I'm going to go see it for sure :)