What if they do? It wouldn't change anything. Life is life and we live it the way we live it. Some shadowy group from fiction being a reality wouldn't be a drop in the bucket to this chaotic ocean we live in. Let people skulk around in the shadows and eventually the light will reveal them. Overall though there is no remote evidence to think that such a group exists in this reality and being afraid of them is like being afraid of the boogeyman. There is always a chance the darkness is hiding something but that doesn't mean there's always something looming in the shadows. Just live your life to the best of your ability and move forward.
It is very easy for people to lay blame on external things when bad things happen. From bad luck to victimhood from others to bad politics to grand conspiracies. But they use that status often to dismiss themselves of responsibility within their own lives.
This is why sayings like 'evil only triumphs so long as good people do nothing.'
Existing or not, maligned or not. No individual entity... no matter how clandestined or 'up the ranks' it is, would ever be able to overmower the mass press of society. History has shown quite readily the dramatic effect of mass human movement. So I think there is little to worry over when it comes to ideas of new-world-order and such. As interesting as the stories can be, it's just another blip in the human narrative.
The Illuminati did -- and still do, to an extent -- exist. The group began in the 'Age of Enlightenment,' a period not only of a shift in political philosophy in many areas of the world, but also a surge in transcendentalist beliefs. Transcendental meditation was very popular through the end of the 18th and early 19th Centuries, and much is reflected in literature of that era. In fact, concepts were still popular in literature through the 1960s. It led to some aspect of the New Age and modern variants of Occultism. But I digress.
Part of the philosophy of the Illuminati is one of exceptionalism -- that the 'enlightened' (which is quite debatable in this context) are somehow better as leadership over the uninlightented. This is what led them to pursue governmental influence. The group began in Bavaria, and spread from there.
The thing is, secret societies in general often sought some influence of governments, from beneath the surface. This has also been the reason people hold such groups as Freemasons in a suspicious light, as many politicians have openly been followers of Freemasonry.
These days, though, there are larger things to worry about, from a political standpoint, than a centuries-old secret society who have all but lost influence. I will not, however, wax political, and therefore will actively avoid the further facts on this matter.