Today's ATC is an entirely different beast, and controllers do on a daily basis what the earliest batch probably would have told you was impossible if you told them this is what their job would look like decades from then. Thousands upon thousands of planes weaving their way along an invisible web in the sky, getting to their destinations with (despite the inevitable grumbling passengers) amazing speed, efficiency, and safety. Take a look at this short (barely over a minute) snapshot of 24 hours worth of airliners traversing the globe:
Since humans tend to be day critters, notice how the video starts off with a stream of airliners heading east from the United States, timed nicely to arrive right around sunrise in Europe. The stream reverses hours later as the flights then travel with the sun, timed to get to the East Coast in the middle of the day. You might also notice around 20 seconds in how thin (relatively speaking) the traffic is over the United States, since that's the dead of night. By about 50 seconds it, once it's become the middle of the U.S. day, the skies are swarming with airliners.
Another nice, short video (this one with some narration) focuses on the air traffic in just the United States for one day:
This second half also shows you what happens when weather interferes with the best-laid plans of mice and men. Starting just after two minutes in, notice how even if they didn't put the weather radar on the depiction, you could still tell where the bad cells are just based on the paths of the planes as they steer around them.
So the next time your flight is delayed because of weather hundreds of miles away from you, instead of sitting around uselessly grumbling and fuming, take another look at these videos and marvel that a system this complex and saturated even works at all! Thanks to the skills of thousands of pilots and controllers working together, combined with a heap of technology like radar, weather observing systems, dispatch scheduling programs, and a partridge in a pear tree, you'll be crammed into a tiny seat paying $7 for an extra soda and getting home safely before you know it.